Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

SSS to show a radius is perpendicular to a chord that it bisects | Geometry | Khan Academy

Video vocabulary

assumption

Copy vocabulary

US / ə'sʌmpʃn /

UK / əˈsʌmpʃən /

A2
  • noun
  • Something you believe to be so, but aren't sure of

forward

Copy vocabulary

US / 'fɔ:wəd /

UK / ˈfɔrwəd /

A1
  • adjecitve
  • Toward what is ahead; in front
  • Acting in a socially aggressive manner; pushy
  • adverb
  • Toward the front in place; in front
  • Toward a future time; to a more advanced state
  • verb
  • To send something to another address or person

other

Copy vocabulary

US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

core

Copy vocabulary

US / kɔ:(r) /

UK / kɔr, kor /

A2
  • noun
  • Important central part of something
  • verb
  • To take out the central section of a fruit

make

Copy vocabulary

US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

construct

Copy vocabulary

US / kənˈstrʌkt /

UK / kənˈstrʌkt /

A2
  • noun
  • A thought, theory or hypothesis
  • verb
  • To build or create something
  • To create a sentence, story, argument or theory

also

Copy vocabulary

US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

how

Copy vocabulary

US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

kind

Copy vocabulary

US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

chord

Copy vocabulary

US / kɔ:d /

UK / kɔrd, kord /

B1
  • noun
  • Line that joins two points on a circle
  • Combination of musical notes played at same time

half

Copy vocabulary

US / hɑ:f /

UK / hæf, hɑf /

A1
  • adjecitve
  • Not complete
  • adverb
  • Partly; somewhat
  • noun
  • One of two equal periods of game time in a sport
  • The part you get when one is divided into two;

axiom

Copy vocabulary

US / ˈæksiəm /

UK / ˈæksiəm /

C1
  • noun
  • A generally accepted rule or statement generally

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

word

Copy vocabulary

US / wɜ:d /

UK / wɚd /

A1
  • noun
  • Unit of language that has a meaning
  • Promise
  • Short remark or piece of information
  • verb
  • To express something by choosing particular words

congruent

Copy vocabulary

US / ˈkɒŋgruənt /

UK / ˈkɑ:ŋgruənt /

C1
  • adjecitve
  • Having the same shape and size

little

Copy vocabulary

US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

lead

Copy vocabulary

US / li:d /

UK / lid /

A1
  • adjecitve
  • Being the main part in movies or plays
  • noun
  • Wire for electricity, computer, etc.; cable
  • Information that could help to solve a crime
  • Main part in a play or movie
  • Heavy, gray metal element
  • Rope used to tie something to stop it escaping
  • Act of being at the front in a race or game
  • verb
  • To show the way or guide others
  • To be at the front of a race or game
  • To travel in front of; go in advance of others

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

might

Copy vocabulary

US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

line

Copy vocabulary

US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

why

Copy vocabulary

US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

worth

Copy vocabulary

US / wɜ:θ /

UK / wɚθ /

A2
  • other
  • the financial, practical or moral value of somebody/something
  • having a particular value, especially in money

split

Copy vocabulary

US / splɪt /

UK / splɪt /

A2
  • adjecitve
  • No longer married or in a relationship
  • (Injured) by cutting it open, as in someone's lip
  • (Of a decision) when people cannot decide a winner
  • noun
  • Difference of opinion in a group causing a break
  • Separation or a break in something
  • verb
  • To become divided or broken along a straight line
  • To cause a cut in (lip, etc.)
  • To have difference of opinion in a group
  • To separate into two or more pieces
  • To divide something in an even or fair way

those

Copy vocabulary

US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

though

Copy vocabulary

US / ðəu /

UK / ðo /

A1
  • adverb
  • Although, despite the fact that

differentiate

Copy vocabulary

US / ˌdɪfə'renʃɪeɪt /

UK / ˌdɪfəˈrɛnʃiˌet /

B1
  • verb
  • To see or show how things are not the same

much

Copy vocabulary

US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

perpendicular

Copy vocabulary

US / ˌpɜ:pənˈdɪkjələ(r) /

UK / ˌpə:pənˈdɪkjəlɚ /

C1
  • adjecitve
  • Being at right angles to a given line or plane

situation

Copy vocabulary

US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

difference

Copy vocabulary

US / 'dɪfrəns /

UK / ˈdɪfərəns, ˈdɪfrəns /

A1
  • noun
  • A thing or issue that people do not agree about
  • Not of the same kind; unlike other things

never

Copy vocabulary

US / 'nevə(r) /

UK / ˈnɛvɚ /

A1
  • adverb
  • Not ever; not at any time

replace

Copy vocabulary

US / rɪ'pleɪs /

UK / rɪˈples /

A2
  • verb
  • To use instead of something else
  • To return an item to its original location

exact

Copy vocabulary

US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

set

Copy vocabulary

US / set /

UK / sɛt /

A1
  • adjecitve
  • Prepared for something; ready
  • noun
  • Complete group of something
  • Place where a television show or movie is filmed
  • Group of games in a tennis match
  • Device that receives radio or television signals
  • verb
  • To make a clock state or ring at a particular time
  • To decide upon or choose something
  • To make something ready for use (e.g. table)
  • To decide on a price for something
  • To become hard (of glue, concrete etc.)
  • To be located in a specific place or time
  • To put (e.g. a vase) down carefully in a place
  • To put someone in a certain condition or state
  • (Of the sun) to go lower than the horizon

well

Copy vocabulary

US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

cool

Copy vocabulary

US / ku:l /

UK / kul /

A1
  • adjecitve
  • Steady and calm when facing difficulties
  • Almost cold; not warm or hot
  • Smart or stylish in a way (young) people admire
  • Unfriendly in an indirect way; distant
  • verb
  • To make something decrease in temperature
  • (Of an emotion, etc.) to become less strongly felt

sorry

Copy vocabulary

US / ˈsɒri /

UK / ˈsɑ:ri /

A1
  • exclamation
  • What you say to admit you were wrong
  • adjecitve
  • Causing others to feel pity; poor
  • Feeling regret or sympathy about wrong thing

clear

Copy vocabulary

US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

problem

Copy vocabulary

US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

Copy vocabulary

US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

center

Copy vocabulary

US / 'sentə /

UK / ˈsɛntɚ /

A1
  • noun
  • Community place people go health or social reasons
  • Place in the middle of something
  • Person or thing that is attracting attention
  • verb
  • To direct focus toward something

secant

Copy vocabulary

US / 'si:kənt /

UK / 'si:kənt /

A1
  • adjecitve
  • Straight line that intersects a curve at two or more points; ratio of the hypotenuse to the adjacent

theorem

Copy vocabulary

US / ˈθɪərəm /

UK / ˈθiərəm, ˈθɪrəm /

B2
  • noun
  • A statement that can be proved

with

Copy vocabulary

US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

diameter

Copy vocabulary

US / daɪˈæmɪtə(r) /

UK / daɪˈæmɪtɚ /

B1
  • noun
  • Distance across the center of an object

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

confuse

Copy vocabulary

US / kənˈfju:z /

UK / kənˈfjuz /

A2
  • verb
  • To make something unclear or hard to understand

last

Copy vocabulary

US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

outer

Copy vocabulary

US / ˈaʊtə(r) /

UK / ˈaʊtɚ /

A1
  • adjecitve
  • Far away
  • Being farther away from the center
  • On or around something; away from the center

draw

Copy vocabulary

US / drɔ: /

UK / drɔ /

A1
  • noun
  • Something that attracts people to visit a place
  • A lottery or prize
  • Result of a game, contest where the score is equal
  • verb
  • To attract attention to someone or something
  • To get closer to or approach something or someone
  • To influence a person's involvement in something
  • To move an object by pulling
  • To create an image using pen or pencil and paper
  • To take one thing out of a container, etc.
  • (Of 2 teams) to finish a game with the same score

hear

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • verb
  • To be aware of sound; to perceive with the ear
  • To be told or find out information or facts
  • To consider or listen to a court case

from

Copy vocabulary

US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

form

Copy vocabulary

US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

out

Copy vocabulary

US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

Copy vocabulary

US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

mathematic

Copy vocabulary

US / ˌmæθɪ'mætɪk /

UK / ˌmæθə'mætɪk /

A1
  • other

share

Copy vocabulary

US / ʃeə(r) /

UK / ʃɛr /

A2
  • noun
  • Part-ownership in a property, business or company
  • Part of a company you own, shown by a certificate
  • verb
  • To divide something between two or more people
  • To allow others to use your things equally
  • To give information, etc. to someone

two

Copy vocabulary

US / tu: /

UK / tu /

A1
  • number
  • 2

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

base

Copy vocabulary

US / beɪs /

UK / bes /

A2
  • noun
  • Place military personnel live, train, and operate
  • Bottom part of an object that touches a surface
  • Unit of counting, e.g. 10 for counting
  • Most important idea or ingredient to add others
  • Origin or start from which something came
  • Main place where an organization or a person works
  • verb
  • To use as the starting point or origin for
  • To have as the main location for (company, etc.)

lot

Copy vocabulary

US / lɒt /

UK / lɑt /

A1
  • noun
  • What happens to a person in life from chance; fate
  • A group of people seen together
  • Item for sale at an auction
  • Small area of land used for a purpose e.g. parking

call

Copy vocabulary

US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

leave

Copy vocabulary

US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

where

Copy vocabulary

US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

picture

Copy vocabulary

US / 'pɪktʃə(r) /

UK / ˈpɪktʃɚ /

A1
  • noun
  • General situation or state of being
  • Mental image of what something is or looks like
  • Movie; film
  • Painting, drawing or photograph on paper or screen
  • verb
  • To understand or imagine something
  • To imagine someone or something in an image

radius

Copy vocabulary

US / ˈreɪdiəs /

UK / ˈrediəs /

B2
  • noun
  • Area around a certain point
  • Long bone on the thumb side of your lower arm
  • Line from the center to the edge of a circle

something

Copy vocabulary

US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

another

Copy vocabulary

US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

correspond

Copy vocabulary

US / ˌkɒrəˈspɒnd /

UK / ˌkɔ:rəˈspɑ:nd /

B1
  • verb
  • To have similarity or equality with something
  • To write letters or emails to someone

sometimes

Copy vocabulary

US / ˈsʌmtaɪmz /

UK / ˈsʌmˌtaɪmz /

A1
  • adverb
  • Only at certain times; occasionally

help

Copy vocabulary

US / help /

UK / hɛlp /

A1
  • noun
  • Something given to enable a person to do something
  • Assistance given to someone in need
  • Someone who makes something easier or possible
  • verb
  • To act to enable a person to do something; assist
  • To make something better or less difficult

particular

Copy vocabulary

US / pəˈtɪkjələ(r) /

UK / pɚˈtɪkjəlɚ, pəˈtɪk- /

B2
  • adjecitve
  • One specific (one)
  • Having firm ideas about what is desirable
  • Being special or more than is typical

think

Copy vocabulary

US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

both

Copy vocabulary

US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

show

Copy vocabulary

US / ʃəʊ /

UK / ʃo /

A1
  • noun
  • False display of love, emotion or action
  • An event for displaying or promoting goods
  • Play, opera or theater production
  • Presentation that is broadcast on TV or radio
  • verb
  • To be easily seen or displayed
  • To display your emotions or feelings
  • To let someone see something; display
  • To explain or teach how something is done
  • To lead someone somewhere; point them to something
  • To prove something to be true, correct
  • To reveal or allow something to be seen

between

Copy vocabulary

US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

add

Copy vocabulary

US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

take

Copy vocabulary

US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

their

Copy vocabulary

US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

useful

Copy vocabulary

US / ˈju:sfl /

UK / ˈjusfəl /

A1
  • adjecitve
  • That can help with a particular task

way

Copy vocabulary

US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

clearly

Copy vocabulary

US / ˈklɪəlɪ /

UK / ˈklɪrlɪ /

A1
  • adverb
  • In a way that is easy to understand; obviously

length

Copy vocabulary

US / leŋθ /

UK / leŋθ /

A2
  • noun
  • Distance from one end of a pool to the other
  • Measurement of distance or of time

pretty

Copy vocabulary

US / 'prɪtɪ /

UK / ˈprɪti /

A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

several

Copy vocabulary

US / ˈsevrəl /

UK / ˈsɛvərəl,ˈsɛvrəl /

A1
  • adjecitve
  • Many of
  • pronoun
  • More than two but not a large amount

bit

Copy vocabulary

US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

look

Copy vocabulary

US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

rewrite

Copy vocabulary

US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

build

Copy vocabulary

US / bɪld /

UK / bɪld /

A1
  • noun
  • Your physical shape; physique
  • verb
  • To establish e.g. a reputation, over time
  • To construct a house, office, factory

confused

Copy vocabulary

US / kənˈfju:zd /

UK / kənˈfjuzd /

A2
  • adjecitve
  • Being hard to understand
  • verb
  • To make something unclear or hard to understand

prove

Copy vocabulary

US / pru:v /

UK / pruv /

A2
  • verb
  • To demonstrate truth by providing evidence

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

rigorously

Copy vocabulary

US / 'rɪɡərəslɪ /

UK / ˈrɪɡərəslɪ /

B1
  • adverb
  • In a thorough manner

about

Copy vocabulary

US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

even

Copy vocabulary

US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

different

Copy vocabulary

US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

Copy vocabulary

US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

essentially

Copy vocabulary

US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

introductory

Copy vocabulary

US / ˌɪntrəˈdʌktəri /

UK / ˌɪntrəˈdʌktəri /

A2
  • adjecitve
  • Serving as an initial experience of something

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

touch

Copy vocabulary

US / tʌtʃ /

UK / tʌtʃ /

A1
  • noun
  • Certain way of doing that makes something special
  • A small amount of something
  • Feeling of a surface
  • verb
  • To affect feelings, especially by causing sympathy
  • To be next to each other with no space between
  • To get involved with (used in negative)
  • To feel an object with your fingers, etc.

adjacent

Copy vocabulary

US / əˈdʒeɪsnt /

UK / əˈdʒesənt /

B1
  • adjecitve
  • Being close or near to a border, wall, or point

example

Copy vocabulary

US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

each

Copy vocabulary

US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

triangle

Copy vocabulary

US / ˈtraɪæŋgl /

UK / ˈtraɪˌæŋɡəl /

B1
  • noun
  • Three people connected with each in a relationship
  • A three-sided piece of metal used in orchestras
  • A closed shape with three straight sides

tell

Copy vocabulary

US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

mean

Copy vocabulary

US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

then

Copy vocabulary

US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

postulate

Copy vocabulary

US / 'pɒstjʊleɪt /

UK / ˈpɑstʃəˌlet /

B2
  • noun
  • Statement forming the basis of a theory
  • verb
  • To claim or suggest so as to begin a debate

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

can

Copy vocabulary

US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

segment

Copy vocabulary

US / ˈsegmənt /

UK / ˈsɛɡmənt /

B1
  • noun
  • Part divided from the other parts of something
  • verb
  • To separate something into different parts

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

give

Copy vocabulary

US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

angle

Copy vocabulary

US / ˈæŋgl /

UK / ˈæŋɡəl /

B1
  • noun
  • Place where two lines or surfaces meet

equal

Copy vocabulary

US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

measure

Copy vocabulary

US / ˈmeʒə(r) /

UK / ˈmɛʒɚ /

A1
  • noun
  • Plan to achieve a desired result
  • Tool used to calculate the size of something
  • verb
  • To determine the value or importance of something
  • To calculate size, weight or temperature of

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

book

Copy vocabulary

US / bʊk /

UK / bʊk /

A1
  • noun
  • Thing made of pages with writing on that you read
  • verb
  • (Police) to officially record someone's crimes
  • To reserve (hotel room, etc.) in advance
  • To produce a red or yellow card to a soccer player

want

Copy vocabulary

US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

video

Copy vocabulary

US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

box

Copy vocabulary

US / bɒks /

UK / bɑ:ks /

A1
  • noun
  • A marked area of a baseball field
  • A container with four straight sides and a lid
  • Area of seating in a theater separated from others
  • A 4 sided container or shape printed on a page
  • Entire amount of something inside a container
  • verb
  • To strike someone on the side of the head
  • To pack an object in a six-sided container
  • To fight with gloved hands as a sport

really

Copy vocabulary

US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

supplementary

Copy vocabulary

US / ˌsʌplɪˈmentri /

UK / ˌsʌplɪˈmentri /

B1
  • adjecitve
  • Functioning in a supporting capacity

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

maybe

Copy vocabulary

US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

our

Copy vocabulary

US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

whole

Copy vocabulary

US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

setup

Copy vocabulary

US / 'setʌp /

UK / ˈsɛtˌʌp /

B2
  • noun
  • Way something is organized or arranged

true

Copy vocabulary

US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

straight

Copy vocabulary

US / streɪt /

UK / stret /

A2
  • adjecitve
  • Not having curves, bends, or angles
  • Not gay; heterosexual
  • honest and direct
  • adverb
  • in a line; immediately; honestly and directly

bisect

Copy vocabulary

US / baɪˈsekt /

UK / baɪ'sekt /

C2
  • verb
  • To cut in half; divide in two

divide

Copy vocabulary

US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

geometry

Copy vocabulary

US / dʒiˈɒmətri /

UK / dʒiˈɑ:mətri /

B2
  • noun
  • Mathematical study of shapes, surfaces, and space
  • Mathematical shape of something

imagine

Copy vocabulary

US / ɪ'mædʒɪn /

UK / ɪˈmædʒɪn /

A1
  • verb
  • To think creatively about; form mental picture of

obviously

Copy vocabulary

US / ˈɒbviəsli /

UK / ˈɑːbviəsli /

A2
  • adverb
  • In a way that is obvious/easy to see or understand

once

Copy vocabulary

US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

while

Copy vocabulary

US / waɪl /

UK / hwaɪl, waɪl /

A1
  • conjunction
  • In spite of the fact that; although
  • During the time that; at the same time
  • noun
  • Short amount of time

point

Copy vocabulary

US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

already

Copy vocabulary

US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

dea

Copy vocabulary

US / di /

UK / /

A1
  • abbreviation
  • Drug Enforcement Administration, an agency of the US Department of Justice.

guess

Copy vocabulary

US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

itself

Copy vocabulary

US / ɪtˈself /

UK / ɪtˈsɛlf /

A1
  • pronoun
  • Referring to it

many

Copy vocabulary

US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

actually

Copy vocabulary

US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

use

Copy vocabulary

US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

write

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

here

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

try

Copy vocabulary

US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

basic

Copy vocabulary

US / 'beɪsɪk /

UK / ˈbesɪk /

A1
  • adjecitve
  • At the most important or easiest (beginner) level

deduce

Copy vocabulary

US / dɪˈdju:s /

UK / dɪˈdu:s /

B2
  • verb
  • To use logic or reason to reach a conclusion

equivalent

Copy vocabulary

US / ɪˈkwɪvələnt /

UK / ɪˈkwɪvələnt /

B1
  • adjecitve
  • Equal to something in value, use or meaning
  • noun
  • Thing like another in quality, quantity or degree

intersect

Copy vocabulary

US / ˌɪntə'sekt /

UK / ˌɪntɚˈsɛkt /

B2
  • verb
  • To divide something by crossing it

knowledge

Copy vocabulary

US / ˈnɒlɪdʒ /

UK / ˈnɑlɪdʒ /

A1
  • noun
  • Information, understanding, or skill

reason

Copy vocabulary

US / 'ri:zn /

UK / ˈrizən /

A1
  • noun
  • Ability to think about facts and form a judgment
  • Explanation for why something occurred or was done
  • verb
  • To think and make conclusions in a logical manner

side

Copy vocabulary

US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

plus

Copy vocabulary

US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero
  • Subtitles section
  • In the last video, we learned that if we have two different triangles, and if all of the corresponding sides of the two triangles have the same length, then by side, side, side, we know that the two triangles are congruent.
  • And I also touched a little bit on the idea of an axiom or postulate, but I want to be clear.
  • Sometimes you will hear this referred to as a side, side, side theorem, and sometimes you'll hear it as a side, postulate, or axiom.
  • And I think it's worth differentiating what these mean.
  • A postulate or an axiom is something that you just assume, you assume from the get-go, while a theorem is something you prove using more basic or using some postulates or axioms.
  • So really, in all of mathematics, you make some core assumptions.
  • You make some core assumptions.
  • You call these the axioms or the postulates.
  • And then using those, you try to prove theorems.
  • So maybe using that one, I can prove some theorem over here, and maybe using that theorem, and then this axiom, I can prove another theorem over here, and then using both of those theorems, I can prove another theorem over here.
  • I think you get the picture.
  • This axiom might lead us to this theorem, and these two might lead us to this theorem right over here.
  • And we essentially try to build our knowledge, or we build a mathematics, around these core assumptions.
  • In an introductory geometry class, we don't rigorously prove side, side, side.
  • We don't rigorously prove the side, side, side theorem.
  • And that's why, in a lot of geometry classes, you kind of just take it as a given, as a postulate or an axiom.
  • And the whole reason why I'm doing this is, one, just so you know the difference between the words theorem and postulate or axiom, and also so that you don't get confused.
  • It is just a given, but in a lot of books, and I've looked at several books, they do refer to it as a side, side, side theorem, even though they never prove it rigorously.
  • They do just assume it.
  • So it really is more of a postulate or an axiom.
  • Now, with that out of the way, we're just going to assume, going forward, that we just know that this is true.
  • We're going to take it as a given.
  • I want to show you that we can already do something pretty useful with it.
  • So let's say that we have a circle, and there's many useful things that we can already do with it.
  • And this circle has a center right here at a.
  • And let's say that we have a chord in this circle that is not a diameter.
  • So let me draw a chord here.
  • So let me draw a chord in the circle.
  • So it's a segment of a secant line.
  • And let's say that I have a line that bisects this chord from the center.
  • I guess I could call it a radius, because I'm going to go from the center to the edge of the circle right over there.
  • So I'm going to the center to the circle itself.
  • And when I say bisects it, so I'm just setting up the problem right now.
  • When I say bisecting it, it means it splits that line segment in half.
  • So what it tells us is that the length of this segment right over here is going to be equivalent to the length of this segment right over there.
  • And what I want to do is, so I've set it up.
  • I have a circle.
  • This radius bisects this chord right over here.
  • And what I want to do is prove that it bisects this chord at a right angle.
  • Or another way to say it, let me add some points here.
  • Let's call this b, let's call this c, and let's call this d.
  • I want to prove that segment AB is perpendicular.
  • It intersects it at a right angle.
  • It is perpendicular to segment CD. And as you can imagine, I'm going to prove it pretty much using the side-side-side, whatever you want to call it.
  • Side-side-side theorem, postulate, or axiom.
  • So let's think about it this way.
  • So you can imagine, if I'm going to use this, I need to have some triangles.
  • There's no triangles here right now.
  • But I can construct triangles, and I can construct triangles based on things I know.
  • For example, I can construct, this has some radius.
  • So let's call this, that's a radius right over here.
  • The length of that is just going to be the radius of the circle.
  • But I can also do it right over here.
  • The length of AC is also going to be the radius of the circle.
  • So we know that these two lines have the same length, which is the radius of the circle.
  • We could say that AD is congruent to AC, or they have the exact same lengths.
  • We know from the setup in the problem that this segment is equal in length to this segment over here.
  • We could even, let me add a point here so I can refer to it, so if I call that point E. We know from the setup in the problem that CE is congruent to ED, or they have the same length.
  • CE has the same length as ED. And we also know that both of these triangles, the one here on the left and the one here on the right, they both share the side EA. So EA is clearly equal to EA. So this is clearly equal to itself.
  • It's the same side.
  • The same side is being used for both triangles.
  • The triangles are adjacent to each other.
  • And so we see a situation where we have two different triangles that have corresponding sides being equal.
  • This side is equivalent to this side right over here.
  • This side is equal in length to that side over there.
  • And then we have, obviously, AE is equivalent to itself.
  • It's a side on both of them.
  • It's the corresponding side on both of these triangles.
  • And so by side, side, side, we know that triangle ABC is congruent to triangle AE.
  • Sorry, it's not ABC.
  • It's AEC.
  • We know, actually, let me write it over here.
  • By side, side, side, we know that triangle AEC is congruent to triangle AED.
  • But how does that help us?
  • Knowing that we used our little theorem, but how does that actually help us here?
  • Well, what's cool is once we know that two triangles are congruent, so because they are congruent, that tells us, so from that, we can deduce that all the angles are the same.
  • And in particular, we can deduce that this angle right over here, that the measure of angle CEA is equivalent to the measure of angle DEA.
  • And the reason why that's useful is that we also see, just by looking at this, that they are supplementary to each other.
  • Their adjacent angles, their outer sides form a straight angle.
  • So CEA is supplementary and equivalent to DEA.
  • So they're also supplementary.
  • So we also have the measure of angle CEA plus the measure of angle DEA is equal to 180 degrees.
  • But they're equivalent to each other.
  • So I could replace the measure of DEA with the measure of CEA, or I could rewrite this as 2 times the measure of angle CEA is equal to 180 degrees.
  • Or I could divide both sides by 2, and I say the measure of angle CEA is equal to 90 degrees, which is going to be the same as the measure of angle DEA.
  • Because they're equivalent.
  • So we know that this angle right over here is 90 degrees.
  • So I can do it with that little box.
  • And this angle right over here is 90 degrees.
  • And because AB intersects where it intersects CD, we have a 90 degree angle here and there.
  • And we can also prove that it's over there as well.
  • They are perpendicular to each other.