# Angles And Points Angles Can Have Points In The Interior, In The Exterior, Or (attractive Interior Math Definition #4)

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### Angles

an•gle1  (anggəl),USA pronunciation n., v.,  -gled, -gling.
n.
1. [Geom.]
• the space within two lines or three or more planes diverging from a common point, or within two planes diverging from a common line.
• the figure so formed.
• the amount of rotation needed to bring one line or plane into coincidence with another, generally measured in radians or in degrees, minutes, and seconds, as in 12° 10prime;
30ʺ, which is read as 12 degrees, 10 minutes, and 30 seconds.
2. an angular projection;
a projecting corner: the angles of a building.
3. a viewpoint;
standpoint: He looked at the problem only from his own angle.
• slant (def. 11).
• the point of view from which copy is written, esp. when the copy is intended to interest a particular audience: The financial editor added a supplementary article from the investor's angle.
4. one aspect of an event, problem, subject, etc.: The accountant emphasized the tax angle of the leasing arrangement.
5. [Motion Pictures, Photog.]See  angle shot.
6. [Informal.]a secret motive: She's been too friendly lately—what's her angle?
7. any of the four interceptions of the equatorial circle by the two basic axes, the horizon and the meridian: commonly identified by the compass directions.
8. See  angle iron (def. 2).
9. [Slang.]play the angles, to use every available means to reach one's goal: A second-rate talent can survive only by playing all the angles.

v.t.
1. to move or bend in an angle.
2. to set, fix, direct, or adjust at an angle: to angle a spotlight.
3. to write or edit in such a way as to appeal to a particular audience;
slant: She angled her column toward teenagers.

v.i.
1. to turn sharply in a different direction: The road angles to the right.
2. to move or go in angles or at an angle: The trout angled downstream.

### And

and (and; unstressed ənd, ən, or, esp. after a homorganic consonant, n),USA pronunciation  conj.
1. (used to connect grammatically coordinate words, phrases, or clauses) along or together with;
as well as;
besides;
also;
moreover: pens and pencils.
plus: 2 and 2 are 4.
3. then: He read for an hour and went to bed.
4. also, at the same time: to sleep and dream.
5. then again;
repeatedly: He coughed and coughed.
6. (used to imply different qualities in things having the same name): There are bargains and bargains, so watch out.
7. (used to introduce a sentence, implying continuation) also;
then: And then it happened.
8. [Informal.]to (used between two finite verbs): Try and do it. Call and see if she's home yet.
9. (used to introduce a consequence or conditional result): He felt sick and decided to lie down for a while. Say one more word about it and I'll scream.
10. but;
on the contrary: He tried to run five miles and couldn't. They said they were about to leave and then stayed for two more hours.
11. (used to connect alternatives): He felt that he was being forced to choose between his career and his family.
12. (used to introduce a comment on the preceding clause): They don't like each other--and with good reason.
13. [Archaic.]if: and you please.Cf. an2.
14. and so forth, and the like;
and others;
et cetera: We discussed traveling, sightseeing, and so forth.
15. and so on, and more things or others of a similar kind;
and the like: It was a summer filled with parties, picnics, and so on.

n.
1. an added condition, stipulation, detail, or particular: He accepted the job, no ands or buts about it.
2. conjunction (def. 5b).

### Angles

an•gle1  (anggəl),USA pronunciation n., v.,  -gled, -gling.
n.
1. [Geom.]
• the space within two lines or three or more planes diverging from a common point, or within two planes diverging from a common line.
• the figure so formed.
• the amount of rotation needed to bring one line or plane into coincidence with another, generally measured in radians or in degrees, minutes, and seconds, as in 12° 10prime;
30ʺ, which is read as 12 degrees, 10 minutes, and 30 seconds.
2. an angular projection;
a projecting corner: the angles of a building.
3. a viewpoint;
standpoint: He looked at the problem only from his own angle.
• slant (def. 11).
• the point of view from which copy is written, esp. when the copy is intended to interest a particular audience: The financial editor added a supplementary article from the investor's angle.
4. one aspect of an event, problem, subject, etc.: The accountant emphasized the tax angle of the leasing arrangement.
5. [Motion Pictures, Photog.]See  angle shot.
6. [Informal.]a secret motive: She's been too friendly lately—what's her angle?
7. any of the four interceptions of the equatorial circle by the two basic axes, the horizon and the meridian: commonly identified by the compass directions.
8. See  angle iron (def. 2).
9. [Slang.]play the angles, to use every available means to reach one's goal: A second-rate talent can survive only by playing all the angles.

v.t.
1. to move or bend in an angle.
2. to set, fix, direct, or adjust at an angle: to angle a spotlight.
3. to write or edit in such a way as to appeal to a particular audience;
slant: She angled her column toward teenagers.

v.i.
1. to turn sharply in a different direction: The road angles to the right.
2. to move or go in angles or at an angle: The trout angled downstream.

### Can

can1  (kan;[unstressed]kən),USA pronunciation auxiliary v.  and v., pres. sing. 1st pers.  can, 2nd  can  or ([Archaic])  canst, 3rd  can, pres. pl.  can*  past sing. 1st pers.  could, 2nd  could  or ([Archaic])  couldst, 3rd  could, past pl.  could. For auxiliary v.: imperative, infinitive, and participles lacking. For v. (Obs.): imperativecan;
infinitivecan;
past part. could;
pres. part.cun•ning.
auxiliary verb.
1. to be able to;
have the ability, power, or skill to: She can solve the problem easily, I'm sure.
2. to know how to: He can play chess, although he's not particularly good at it.
3. to have the power or means to: A dictator can impose his will on the people.
4. to have the right or qualifications to: He can change whatever he wishes in the script.
5. may;
have permission to: Can I speak to you for a moment?
6. to have the possibility: A coin can land on either side.

v.t., v.i.
1. [Obs.]to know.

### Have

have (hav;[unstressed]həv, əv* [for 26 usually]haf ),USA pronunciation v.  and auxiliary v., pres. sing. 1st pers.  have, 2nd  have  or ([Archaic])  hast, 3rd  has  or ([Archaic])  hath, pres. pl.  have*  past sing. 1st pers.  had, 2nd  had  or ([Archaic]) ) hadst  or  had•dest, 3rd  had, past pl.  had;
pres. part.  hav•ing, n.
v.t.
1. to possess;
own;
hold for use;
contain: He has property. The work has an index.
2. to hold, possess, or accept in some relation, as of kindred or relative position: He wanted to marry her, but she wouldn't have him.
3. to get, receive, or take: to have a part in a play; to have news.
4. to experience, undergo, or endure, as joy or pain: Have a good time. He had a heart attack last year.
5. to hold in mind, sight, etc.: to have doubts.
6. to cause to, as by command or invitation: Have him come here at five.
7. to be related to or be in a certain relation to: She has three cousins. He has a kind boss.
8. to show or exhibit in action or words: She had the crust to refuse my invitation.
9. to be identified or distinguished by;
possess the characteristic of: He has a mole on his left cheek. This wood has a silky texture.
10. to engage in or carry on: to have a talk; to have a fight.
11. to partake of;
eat or drink: He had cake and coffee for dessert.
12. to permit or allow: I will not have any talking during the concert.
13. to assert, maintain, or represent as being: Rumor has it that she's going to be married.
14. to know, understand, or be skilled in: to have neither Latin nor Greek.
15. to beget or give birth to: to have a baby.
16. to hold an advantage over: He has you there.
17. to outwit, deceive, or cheat: We realized we'd been had by an expert con artist.
18. to control or possess through bribery;
bribe.
19. to gain possession of: There is none to be had at that price.
20. to hold or put in a certain position or situation: The problem had me stumped. They had him where they wanted him.
21. to exercise, display, or make use of: Have pity on him.
22. to invite or cause to be present as a companion or guest: We had Evelyn and Everett over for dinner. He has his bodyguard with him at all times.
23. to engage in sexual intercourse with.

v.i.
1. to be in possession of money or wealth: There are some who have and some who have not.

auxiliary verb.
1. (used with a past participle to form perfect tenses): She has gone. It would have been an enjoyable party if he hadn't felt downcast.
2. to be required, compelled, or under obligation (fol. by infinitival to, with or without a main verb): I have to leave now. I didn't want to study, but I had to.
3. had better or  best, ought to: You'd better go now, it's late.
4. had rather. See  rather (def. 8).
5. have at, to go at vigorously;
attack: First he decided to have at his correspondence.
6. have done, to cease;
finish: It seemed that they would never have done with their struggle.
• to become weary of or disgusted with whatever one has been doing: I've been working like a fool, but now I've had it.
• to suffer defeat;
fail: He was a great pitcher, but after this season he'll have had it.
• to have missed a last opportunity: He refused to take any more excuses and told them all that they'd had it.
• to become unpopular or passé: Quiz shows have had it.
8. have it coming, to merit or deserve: When they lost their fortune, everyone said that they had it coming.
9. have it in for, to plan or wish to do something unpleasant to;
hold a grudge against: She has it in for intelligent students who fail to use their abilities.
10. have it out, to come to an understanding or decision through discussion or combat: We've been in disagreement about this for a long time, and I think we should have it out, once and for all.
11. have on:
• to be clothed in;
be wearing: She had on a new dress.
• to have arranged or planned: What do you have on for Christmas?
• to tease (a person);
make the butt of a joke. Cf. put (def. 34).
12. have to do with:
• to be connected or associated with: Your lack of confidence probably had a lot to do with your not getting the job.
• to deal with;
be concerned with: I will have nothing to do with their personal squabbles.
13. to have and to hold, to possess legally;
have permanent possession of: The house, with the mortgage finally paid, was at last their own to have and to hold.

n.
1. Usually,  haves. an individual or group that has wealth, social position, or other material benefits (contrasted with have-not).

### In

prep.
1. (used to indicate inclusion within space, a place, or limits): walking in the park.
2. (used to indicate inclusion within something abstract or immaterial): in politics; in the autumn.
3. (used to indicate inclusion within or occurrence during a period or limit of time): in ancient times; a task done in ten minutes.
4. (used to indicate limitation or qualification, as of situation, condition, relation, manner, action, etc.): to speak in a whisper; to be similar in appearance.
5. (used to indicate means): sketched in ink; spoken in French.
6. (used to indicate motion or direction from outside to a point within) into: Let's go in the house.
7. (used to indicate transition from one state to another): to break in half.
8. (used to indicate object or purpose): speaking in honor of the event.
9. in that, because;
inasmuch as: In that you won't have time for supper, let me give you something now.

1. in or into some place, position, state, relation, etc.: Please come in.
2. on the inside;
within.
3. in one's house or office.
4. in office or power.
5. in possession or occupancy.
6. having the turn to play, as in a game.
7. [Baseball.](of an infielder or outfielder) in a position closer to home plate than usual;
short: The third baseman played in, expecting a bunt.
8. on good terms;
in favor: He's in with his boss, but he doubts it will last.
9. in vogue;
in style: He says straw hats will be in this year.
10. in season: Watermelons will soon be in.
11. be in for, to be bound to undergo something, esp. a disagreeable experience: We are in for a long speech.
12. in for it, [Slang.]about to suffer chastisement or unpleasant consequences, esp. of one's own actions or omissions: I forgot our anniversary again, and I'll be in for it now.Also,[Brit.,] for it.
13. in with, on friendly terms with;
familiar or associating with: They are in with all the important people.

1. located or situated within;
inner;
internal: the in part of a mechanism.
2. [Informal.]
• in favor with advanced or sophisticated people;
fashionable;
stylish: the in place to dine; Her new novel is the in book to read this summer.
• comprehensible only to a special or ultrasophisticated group: an in joke.
3. well-liked;
included in a favored group.
4. inward;
incoming;
inbound: an in train.
5. plentiful;
available.
6. being in power, authority, control, etc.: a member of the in party.
7. playing the last nine holes of an eighteen-hole golf course (opposed to out): His in score on the second round was 34.

n.
1. Usually,  ins. persons in office or political power (distinguished from outs).
2. a member of the political party in power: The election made him an in.
3. pull or influence;
a social advantage or connection: He's got an in with the senator.
4. (in tennis, squash, handball, etc.) a return or service that lands within the in-bounds limits of a court or section of a court (opposed to out).

v.t. Brit. [Dial.]
1. to enclose.

### The

the1  (stressed ᵺē; unstressed before a consonant ᵺə;
unstressed before a vowel ᵺē),USA pronunciation
definite article.
1. (used, esp. before a noun, with a specifying or particularizing effect, as opposed to the indefinite or generalizing force of the indefinite article a or an): the book you gave me; Come into the house.
2. (used to mark a proper noun, natural phenomenon, ship, building, time, point of the compass, branch of endeavor, or field of study as something well-known or unique):the sun;
the Alps;
theQueen Elizabeth;
the past; the West.
3. (used with or as part of a title): the Duke of Wellington; the Reverend John Smith.
4. (used to mark a noun as indicating the best-known, most approved, most important, most satisfying, etc.): the skiing center of the U.S.; If you're going to work hard, now is the time.
5. (used to mark a noun as being used generically): The dog is a quadruped.
6. (used in place of a possessive pronoun, to note a part of the body or a personal belonging): He won't be able to play football until the leg mends.
7. (used before adjectives that are used substantively, to note an individual, a class or number of individuals, or an abstract idea): to visit the sick; from the sublime to the ridiculous.
8. (used before a modifying adjective to specify or limit its modifying effect): He took the wrong road and drove miles out of his way.
9. (used to indicate one particular decade of a lifetime or of a century): the sixties; the gay nineties.
10. (one of many of a class or type, as of a manufactured item, as opposed to an individual one): Did you listen to the radio last night?
11. enough: He saved until he had the money for a new car. She didn't have the courage to leave.
12. (used distributively, to note any one separately) for, to, or in each;
a or an: at one dollar the pound.

### In

prep.
1. (used to indicate inclusion within space, a place, or limits): walking in the park.
2. (used to indicate inclusion within something abstract or immaterial): in politics; in the autumn.
3. (used to indicate inclusion within or occurrence during a period or limit of time): in ancient times; a task done in ten minutes.
4. (used to indicate limitation or qualification, as of situation, condition, relation, manner, action, etc.): to speak in a whisper; to be similar in appearance.
5. (used to indicate means): sketched in ink; spoken in French.
6. (used to indicate motion or direction from outside to a point within) into: Let's go in the house.
7. (used to indicate transition from one state to another): to break in half.
8. (used to indicate object or purpose): speaking in honor of the event.
9. in that, because;
inasmuch as: In that you won't have time for supper, let me give you something now.

1. in or into some place, position, state, relation, etc.: Please come in.
2. on the inside;
within.
3. in one's house or office.
4. in office or power.
5. in possession or occupancy.
6. having the turn to play, as in a game.
7. [Baseball.](of an infielder or outfielder) in a position closer to home plate than usual;
short: The third baseman played in, expecting a bunt.
8. on good terms;
in favor: He's in with his boss, but he doubts it will last.
9. in vogue;
in style: He says straw hats will be in this year.
10. in season: Watermelons will soon be in.
11. be in for, to be bound to undergo something, esp. a disagreeable experience: We are in for a long speech.
12. in for it, [Slang.]about to suffer chastisement or unpleasant consequences, esp. of one's own actions or omissions: I forgot our anniversary again, and I'll be in for it now.Also,[Brit.,] for it.
13. in with, on friendly terms with;
familiar or associating with: They are in with all the important people.

1. located or situated within;
inner;
internal: the in part of a mechanism.
2. [Informal.]
• in favor with advanced or sophisticated people;
fashionable;
stylish: the in place to dine; Her new novel is the in book to read this summer.
• comprehensible only to a special or ultrasophisticated group: an in joke.
3. well-liked;
included in a favored group.
4. inward;
incoming;
inbound: an in train.
5. plentiful;
available.
6. being in power, authority, control, etc.: a member of the in party.
7. playing the last nine holes of an eighteen-hole golf course (opposed to out): His in score on the second round was 34.

n.
1. Usually,  ins. persons in office or political power (distinguished from outs).
2. a member of the political party in power: The election made him an in.
3. pull or influence;
a social advantage or connection: He's got an in with the senator.
4. (in tennis, squash, handball, etc.) a return or service that lands within the in-bounds limits of a court or section of a court (opposed to out).

v.t. Brit. [Dial.]
1. to enclose.

### The

the1  (stressed ᵺē; unstressed before a consonant ᵺə;
unstressed before a vowel ᵺē),USA pronunciation
definite article.
1. (used, esp. before a noun, with a specifying or particularizing effect, as opposed to the indefinite or generalizing force of the indefinite article a or an): the book you gave me; Come into the house.
2. (used to mark a proper noun, natural phenomenon, ship, building, time, point of the compass, branch of endeavor, or field of study as something well-known or unique):the sun;
the Alps;
theQueen Elizabeth;
the past; the West.
3. (used with or as part of a title): the Duke of Wellington; the Reverend John Smith.
4. (used to mark a noun as indicating the best-known, most approved, most important, most satisfying, etc.): the skiing center of the U.S.; If you're going to work hard, now is the time.
5. (used to mark a noun as being used generically): The dog is a quadruped.
6. (used in place of a possessive pronoun, to note a part of the body or a personal belonging): He won't be able to play football until the leg mends.
7. (used before adjectives that are used substantively, to note an individual, a class or number of individuals, or an abstract idea): to visit the sick; from the sublime to the ridiculous.
8. (used before a modifying adjective to specify or limit its modifying effect): He took the wrong road and drove miles out of his way.
9. (used to indicate one particular decade of a lifetime or of a century): the sixties; the gay nineties.
10. (one of many of a class or type, as of a manufactured item, as opposed to an individual one): Did you listen to the radio last night?
11. enough: He saved until he had the money for a new car. She didn't have the courage to leave.
12. (used distributively, to note any one separately) for, to, or in each;
a or an: at one dollar the pound.

### Or

or1  (ôr; unstressed ər),USA pronunciation  conj.
1. (used to connect words, phrases, or clauses representing alternatives): books or magazines; to be or not to be.
2. (used to connect alternative terms for the same thing): the Hawaiian, or Sandwich, Islands.
3. (used in correlation): either … or; or … or; whether … or.
4. (used to correct or rephrase what was previously said): His autobiography, or rather memoirs, will soon be ready for publication.
5. otherwise;
or else: Be here on time, or we'll leave without you.
6. [Logic.]the connective used in disjunction.

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