Theorem 3.4 Alternate Interior Angles Converse: If Two Lines Are Cut By A Transversal So ( Alternate Exterior And Interior Angles #5)

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Theorem 3.4 Alternate Interior Angles Converse: If Two Lines Are Cut By A Transversal So ( Alternate Exterior And Interior Angles #5)

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Theorem 3.4 Alternate Interior Angles Converse: If Two Lines Are Cut By A Transversal So ( Alternate Exterior And Interior Angles #5) Photos Album

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Alternate

al•ter•nate (v. ôltər nāt′, al-;adj., n. ôltər nit, al-),USA pronunciation v.,  -nat•ed, -nat•ing, adj., n. 
v.i. 
  1. to interchange repeatedly and regularly with one another in time or place;
    rotate (usually fol. by with): Day alternates with night.
  2. to change back and forth between conditions, states, actions, etc.: He alternates between hope and despair.
  3. to take turns: My sister and I alternated in doing the dishes.
  4. to reverse direction or sign periodically.
  5. to occur as a variant in alternation with another form.

v.t. 
  1. to perform or do in succession or one after another: to alternate comedy acts; to alternate jogging and walking.
  2. to interchange successively or regularly: to alternate hot and cold compresses.

adj. 
  1. being in a constant state of succession or rotation;
    interchanged repeatedly one for another: Winter and summer are alternate seasons.
  2. reciprocal;
    mutual: alternate acts of kindness.
  3. every second one of a series: Read only the alternate lines.
  4. constituting an alternative: The alternate route is more scenic.
  5. alternative (defs. 4, 6).
  6. [Bot.]
    • placed singly at different heights on the axis, on each side in succession, or at definite angular distances from one another, as leaves.
    • opposite to the intervals between other organs: petals alternate with sepals.

n. 
  1. a person authorized to fill the position, exercise the duties, etc., of another who is temporarily absent;
    substitute.
  2. [Theat.]
    • either of two actors who take turns playing the same role.
    • an understudy.
  3. alternative.
alter•nate•ly, adv. 
alter•nate•ness, n. 
alter•nat′ing•ly, adv. 

Interior

in•te•ri•or (in tērē ər),USA pronunciation adj. 
  1. being within; inside of anything;
    internal;
    inner;
    further toward a center: the interior rooms of a house.
  2. of or pertaining to that which is within;
    inside: an interior view.
  3. situated well inland from the coast or border: the interior towns of a country.
  4. of or pertaining to the inland.
  5. domestic: interior trade.
  6. private or hidden;
    inner: interior negotiations of the council.
  7. pertaining to the mind or soul;
    mental or spiritual: the interior life.

n. 
  1. the internal or inner part;
    inside.
    • the inside part of a building, considered as a whole from the point of view of artistic design or general effect, convenience, etc.
    • a single room or apartment so considered.
  2. a pictorial representation of the inside of a room.
  3. the inland parts of a region, country, etc.: the Alaskan interior.
  4. the domestic affairs of a country as distinguished from its foreign affairs: the Department of the Interior.
  5. the inner or inward nature or character of anything.
  6. the largest open set contained in a given set, as the points in a circle not including the boundary.

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.

If

if (if ),USA pronunciation conj. 
  1. in case that;
    granting or supposing that;
    on condition that: Sing if you want to. Stay indoors if it rains. I'll go if you do.
  2. even though: an enthusiastic if small audience.
  3. whether: He asked if I knew Spanish.
  4. (used to introduce an exclamatory phrase): If only Dad could see me now!
  5. when or whenever: If it was raining, we had to play inside.

n. 
  1. a supposition;
    uncertain possibility: The future is full of ifs.
  2. a condition, requirement, or stipulation: There are too many ifs in his agreement.
  3. ifs, ands, or buts, reservations, restrictions, or excuses: I want that job finished today, and no ifs, ands, or buts.

Two

two (to̅o̅),USA pronunciation  n. 
  1. a cardinal number, 1 plus 1.
  2. a symbol for this number, as 2 or II.
  3. a set of this many persons or things.
  4. a playing card, die face, or half of a domino face with two pips.
  5. in two, into two separate parts, as halves: A bolt of lightning split the tree in two.
  6. put two and two together, to draw a correct conclusion from the given circumstances;
    infer: It didn't require a great mind to put two and two together.

adj. 
  1. amounting to two in number.

Are

are1  (är; unstressed ər),USA pronunciation v. 
  • pres. indic. pl. and 2nd pers. sing. of  be. 
  • Cut

    cut (kut),USA pronunciation v.,  cut, cut•ting, adj., n. 
    v.t. 
    1. to penetrate with or as if with a sharp-edged instrument or object: He cut his finger.
    2. to divide with or as if with a sharp-edged instrument;
      sever;
      carve: to cut a rope.
    3. to detach with or as if with a sharp-edged instrument;
      separate from the main body;
      lop off: to cut a slice from a loaf of bread.
    4. to hew or saw down;
      fell: to cut timber.
    5. to trim by clipping, shearing, paring, or pruning: to cut hair.
    6. to mow;
      reap;
      harvest: to cut grain.
    7. to abridge or shorten;
      edit by omitting a part or parts: to cut a speech.
    8. to lower, reduce, diminish, or curtail (sometimes fol. by down): to cut prices.
    9. to dilute;
      make less thick: to cut wine.
    10. to dissolve: That detergent cuts grease effectively.
    11. to intersect;
      cross: One line cuts another at right angles.
    12. to cease;
      discontinue (often fol. by out): Cut the kidding. Let's cut out the pretense.
    13. to stop;
      halt the running of, as a liquid or an engine (often fol. by off): The pilot cut the engines and glided in for a landing. Cut off the hot water.
    14. to dilute or adulterate (a drug) by mixing it with other substances.
    15. to grow (a tooth or teeth) through the gum: The baby is cutting his teeth.
    16. to type, write, or draw on (a stencil) for mimeographing.
    17. to make or fashion by cutting, as a statue, jewel, or garment.
    18. [Glassmaking.]to produce a pattern (in glass) by grinding and polishing.
    19. to refuse to recognize socially;
      shun ostentatiously: Her friends began to cut her as the season progressed.
    20. to strike sharply, as with a whip.
    21. to absent oneself from: allowed to cut three classes per semester.
    22. [Motion Pictures, Television.]
      • to stop (a scene or shot being filmed).
      • to edit (a film).
    23. to wound the feelings of severely.
    24. [Cards.]
      • to divide (a pack of cards) at random into two or more parts, by removing cards from the top.
      • to take (a card) from a deck.
    25. to record a selection on (a phonograph record or tape);
      make a recording of.
    26. to castrate or geld.
    27. to hit (a ball) with either the hand or some instrument so as to change its course and often to cause it to spin.
    28. to hollow out;
      excavate;
      dig: to cut a trench.
    29. [Cricket.]to strike and send off (a ball) in front of the batsman, and parallel to the wicket.
    30. to be a nonplaying dealer, manager, or supervisor of (a card game, crap game, or other gambling game) in return for a percentage of the money bet or sometimes for a fee.

    v.i. 
    1. to penetrate or divide something, as with a sharp-edged instrument;
      make an incision: The scissors cut well.
    2. to admit of being cut: Butter cuts easily.
    3. to pass, go, or come, esp. in the most direct way (usually fol. by across, through, in, etc.): to cut across an empty lot.
    4. [Motion Pictures, Television.]
      • to shift suddenly from one shot to another: Cut to the barroom interior.
      • to stop the action of a scene: used as a command by a director.
    5. to make a sudden or sharp turn in direction;
      change direction suddenly;
      swerve: We cut to the left to avoid hitting the child.
    6. to strike a person, animal, etc., sharply, as with a whip.
    7. to wound the feelings severely: His criticism cut deep.
    8. (of the teeth) to grow through the gums.
    9. [Cards.]to cut the cards.
    10. to leave hastily: to cut for the hills.
    11. (of a horse) to interfere.
    12. cut a caper or  figure, to perform a spirited, brief, outlandish dance step, esp. as a result of euphoria.
    13. cut across, to precede or go beyond considerations of;
      transcend: The new tax program cuts across party lines.
    14. cut a figure: 
      • See  cut a caper. 
      • to give a certain impression of oneself: He cut a distinguished figure in his tuxedo.
    15. cut and run: 
      • [Naut.]to cut the anchor cable and set sail, as in an emergency.
      • to leave as hurriedly as possible;
        flee.
    16. cut back: 
      • to shorten by cutting off the end.
      • to curtail or discontinue: Steel production has been cut back in recent months.
      • to return to an earlier episode or event, as in the plot of a novel.
      • [Football.]to reverse direction suddenly by moving in the diagonally opposite course.
    17. cut both ways, to have, produce, or result in advantages as well as disadvantages: This decision will inevitably cut both ways.
    18. cut down: 
      • Also,  cut down on. to lessen;
        decrease: to cut down on between-meal snacks.
      • to strike and cause to fall: The first force to attempt an advance was swiftly cut down.
      • to destroy, kill, or disable: The hurricane cut down everything in its path.
      • to remodel, remake, or reduce in size, as a garment: She had her old coat cut down to fit her daughter.
    19. cut or  chop down to size, to reduce the stature or importance of: The novelist had a big ego until the critics cut him down to size.
    20. cut in: 
      • to move or thrust oneself, a vehicle, etc., abruptly between others: A speeding car cut in and nearly caused an accident.
      • to interpose;
        interrupt: to cut in with a remark.
      • to interrupt a dancing couple in order to dance with one of them.
      • to blend (shortening) into flour by means of a knife.
    21. cut it, [Informal.]
      • to achieve or maintain a desired level of performance: The aging football player decided he couldn't cut it any longer and retired.
      • to be effective or successful;
        satisfy a need.
    22. cut it out, [Informal.]to stop doing something: That hurts! Cut it out!
    23. cut no ice. See  ice (def. 10).
    24. cut off: 
      • to intercept.
      • to interrupt.
      • to stop suddenly;
        discontinue.
      • to halt the operation of;
        turn off.
      • to shut off or shut out.
      • to disinherit.
      • to sever;
        separate.
    25. cut out: 
      • to omit;
        delete;
        excise.
      • to oust and replace a rival;
        supplant.
      • to part an animal from a herd.
      • to plan;
        arrange: He has his work cut out for him.
      • to move out of one's lane of traffic.
      • Also,  cut on out. to leave suddenly.
      • to refrain from;
        stop: to cut out smoking.
      • (of an engine, machine, etc.) to stop running.
    26. cut up: 
      • to cut into pieces or sections.
      • to lacerate;
        wound.
      • to distress mentally;
        injure.
      • to play pranks;
        misbehave: They got scolded for cutting up in church.

    adj. 
    1. that has been subjected to cutting;
      divided into pieces by cutting;
      detached by cutting: cut flowers.
    2. fashioned by cutting;
      having the surface shaped or ornamented by grinding, polishing, or the like: cut diamonds.
    3. reduced by or as if by cutting: cut whiskey; cut prices.
    4. incised;
      cleft.
    5. castrated;
      gelded.
    6. drunk.
    7. cut out for, fitted for;
      capable of: He wasn't cut out for military service.

    n. 
    1. the act of cutting;
      a stroke or a blow, as with a knife, whip, etc.
    2. the result of cutting, as an incision, wound, passage, or channel.
    3. a piece cut off: a cut of a pie.
    4. a share, esp. of earnings or profits: His agent's cut is 20 percent.
    5. a haircut, often with a styling.
    6. a reduction in price, salary, etc.
    7. the manner or fashion in which anything is cut: the cut of a dress.
    8. style;
      manner;
      kind: We need a man of his cut in this firm.
    9. a passage or course straight across or through: a cut through the woods.
    10. an excision or omission of a part.
    11. a part or quantity of text deleted or omitted.
    12. a quantity cut, esp. of lumber.
    13. a refusal to recognize an acquaintance.
    14. an act, speech, etc., that wounds the feelings.
    15. an engraved plate or block of wood used for printing.
    16. a printed picture or illustration.
    17. an absence, as from a school class, at which attendance is required.
    18. [Butchering.]part of an animal usually cut as one piece.
    19. [Cards.]a cutting of the cards.
      • the act of cutting a ball.
      • the spin imparted.
    20. [Fencing.]a blow with the edge of the blade instead of the tip.
    21. one of several pieces of straw, paper, etc., used in drawing lots.
    22. [Motion Pictures, Television.]
      • the instantaneous or gradual transition from one shot or scene to another in an edited film.
      • an edited version of a film. Cf. rough cut, final cut.
      • an act or instance of editing a film.
    23. an individual song, musical piece, or other similar material on a record or tape.
    24. any product of the fractional distillation of petroleum.
    25. a cut above, somewhat superior to another (thing, person, etc.) in some respect: Her work is a cut above anyone else's.

    By

    by1  (bī),USA pronunciation prep., adv., adj., n., pl.  byes. 
    prep. 
    1. near to or next to: a home by a lake.
    2. over the surface of, through the medium of, along, or using as a route: He came by the highway. She arrived by air.
    3. on, as a means of conveyance: They arrived by ship.
    4. to and beyond the vicinity of;
      past: He went by the church.
    5. within the extent or period of;
      during: by day; by night.
    6. not later than;
      at or before: I usually finish work by five o'clock.
    7. to the extent or amount of: The new tug is larger than the old one by a great deal. He's taller than his sister by three inches.
    8. from the opinion, evidence, or authority of: By his own account he was in Chicago at the time. I know him by sight.
    9. according to;
      in conformity with: This is a bad movie by any standards.
    10. with (something) at stake;
      on: to swear by all that is sacred.
    11. through the agency, efficacy, work, participation, or authority of: The book was published by Random House.
    12. from the hand, mind, invention, or creativity of: She read a poem by Emily Dickinson. The phonograph was invented by Thomas Edison.
    13. in consequence, as a result, or on the basis of: We met by chance. We won the game by forfeit.
    14. accompanied with or in the atmosphere of: Lovers walk by moonlight.
    15. in treatment or support of;
      for: He did well by his children.
    16. after;
      next after, as of the same items in a series: piece by piece; little by little.
    17. (in multiplication) taken the number of times as that specified by the second number, or multiplier: Multiply 18 by 57.
    18. (in measuring shapes) having an adjoining side of, as a width relative to a length: a room 10 feet by 12 feet.
    19. (in division) separated into the number of equal parts as that specified by the second number, or divisor: Divide 99 by 33.
    20. in terms or amounts of;
      in measuring units of: Apples are sold by the bushel. I'm paid by the week.
    21. begot or born of: Eve had two sons by Adam.
    22. (of quadrupeds) having as a sire: Equipoise II by Equipoise.
    23. [Navig.](as used in the names of the 16 smallest points on the compass) one point toward the east, west, north, or south of N, NE, E, SE, S, SW, W, or NW, respectively: He sailed NE by N from Pago Pago.
    24. into, at, or to: Come by my office this afternoon.

    adv. 
    1. near;
      in the immediate vicinity;
      at hand: The school is close by.
    2. to and beyond a point near something;
      past: The car drove by.
    3. aside;
      away: Put your work by for the moment. Over the years, she laid by enough money to retire.
    4. over;
      past: in times gone by.
    5. by and by, in a short time;
      before long;
      presently: The clouds will disappear by and by.
    6. by and large, in general;
      on the whole: By and large, there is much to be said for the new system.
    7. by me: 
      • (in bridge and other bidding card games) a declaration that the speaker is passing.
      • (in poker) a declaration that the speaker is checking: Is my pair of tens still high? By me.

    adj. Also,  bye. 
    1. situated to one side: They came down a by passage.
    2. secondary, incidental: It was only a by comment.

    n. 
    1. bye1.
    2. by the by. See  bye 1 (def. 5).

    So

    so1  (sō),USA pronunciation adv. 
    1. in the way or manner indicated, described, or implied: Do it so.
    2. in that or this manner or fashion;
      thus: So it turned out.
    3. in the aforesaid state or condition: It is broken and has long been so.
    4. to the extent or degree indicated or suggested: Do not walk so fast.
    5. very or extremely: I'm so sad.
    6. very greatly: My head aches so!
    7. (used before an adverb or an adverbial clause and fol. by as) to such a degree or extent: so far as I know.
    8. having the purpose of: a speech so commemorating the victory.
    9. for this or that reason;
      hence;
      therefore: She is ill, and so cannot come to the party.
    10. (used as an affirmative to emphasize or confirm a previous statement) most certainly: I said I would come, and so I will.
    11. (used as an emphatic affirmative to contradict a previous statement) indeed;
      truly;
      too: I was so at the party!
    12. likewise or correspondingly;
      also;
      too: If he is going, then so am I.
    13. in such manner as to follow or result from: As he learned, so did he teach.
    14. in the way that follows;
      in this way: The audience was seated, and so the famous speech began.
    15. in the way that precedes;
      in that way: So ended the speech, and the listeners arose and cheered.
    16. in such way as to end in: So live your life that old age will bring you no regrets.
    17. then;
      subsequently: and so to bed.
    18. so much as, even: He doesn't so much as say hello to me.
    19. so as: 
      • with the result or purpose: to turn up the volume of the radio so as to drown out the noise from the next apartment.
      • [Older Use.]provided that: I like any flower, just so as it's real.
    20. only or  just so many, being a limited or small number or amount: I can eat only so many pieces of fruit.
    21. only or  just so much, being a limited amount or quantity;
      up to a certain point or maximum: I can eat only so much fruit; just so much that one can do in such a case.
    22. so to speak. See  speak (def. 20).
    23. so what? See  what (def. 17).

    conj. 
    1. in order that (often fol. by that): Check carefully, so any mistakes will be caught.
    2. with the result that (often fol. by that): He checked carefully, so that the mistakes were caught.
    3. on the condition that;
      if.

    pron. 
    1. such as has been stated: to be good and stay so.
    2. something that is about or near the persons or things in question, as in number or amount: Of the original twelve, five or so remain.
    3. so much: 
      • something, as an amount or cost, that is not specified or determined: The carpeting is priced at so much per yard.
      • all that is or needs to be said or done: So much for the preliminaries, let's get down to the real issues.

    interj. 
    1. (used as an exclamation of surprise, shock, discovery, inquiry, indifference, etc., according to the manner of utterance.)

    adj. 
    1. true as stated or reported;
      conforming with reality or the fact: Say it isn't so.

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