Part I. Use Figure 1 to complete the sentence or phrase. 1) Ll and L are vertical angles.

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1 Geometry Chapter3Review2()\~ Name _ Please show all work for full credit. Period -- Date Part. Use Figure to complete the sentence or phrase. ) Ll and L are vertical angles. 2) L2 and L are corresponding angles. 3) L6 and L are alternate interior angles. J! 4) -L7 and L6 are angles. 5) L5 and L4 are angles. 6) f ml5 =20, then ml6 =. 7) f ml3 = 35, then ml2 = Figure 8) f ml8 = 20, then ml5 = Part. Use Figure 2 to determine the type of angles listed below. 9) Ll and L4 0) L2 and L3 ) Ll and L2 2) L3 and L5 Part. Use Figure 3 to answer the following questions. j k and m n Figure 2 3) f mll = 30, then ml9 =. 4) f ml9 = 80, then ml6 =. 5) f ml2 = 5, then ml5 =. 6) f ml2 = 2x + 5 and ml4 = 3x - 40, find x. 7) f ml3 = 2x -0 and ml7 = 3x+ 25, find x. m n Figure 3 Part V. Find the value ofx so that line m is parallel to line n. 8) 9) Geometry Ch 3 Review m

2 Part V. Mark each questions True or False. fit is false, state why. 3) The slope ofa verticaine is always zero. 32) Skew lines never intersect. 33) Alternate exterior angles are congruent. 34) f alternate interior angles are congruent, then the lines are parallel. 35) Corresponding angles are congruent. 36) The slope ofparallel lines are the same. 37) Vertical angles are supplementary. 38) Alternate interior angles have a common vertex. Part V. Use Figure 5. The first step in each of the questions is given. Name the theorem, postulate, or definition that makes the second statement true. 39) a. Ll ~ L5 a. Given b. mil n b. _ 40) a. Ll, L2 a. Given b. Ll~L2 b. _ 4) a. mil n a. Given b. Ll ~ L6 b. _ 42) a. L2 and L8 are supplementary a. Given b. mlln b. Part X. Use Figure 6. PS - SQ, PQ - QR, and QR - SR. Name the segment whose length represents the distance between the following pairs of lines. 43) Pto SQ Q rt' :::...p 44) R to PQ 45) Qto SR Figure 6 46) S to QR R s Geometry Ch 3 Review 3

3 ll X: Proofs - Fill in the blanks of the proofs. ~. Given: m Prove: ml + ml3 =80 Statements. m 2. Ll =L2. Given 2. Reasons ~ / i / 2/~..~ / -: _ ~ of _ 3. Definition of congruent angles 4. L2 and L3 are a linear pair 4. _ 5. _ 5. _ 6. ml2 + ml3 = _ 7. ml + ml3 = _. Given: mll+ml4=80 Prove: m / ~ j / 3 / /4 m, --.. Statements Reasons. mll+ml4 =80. Given 2. Ll and L2 are a linear pair , ml + ml2 = mll+ml4= 5. Substitution Subtraction 7. L4=L m 8. Page 5 of6

4 Answers: Corresponding angles postulate 3. mll=ml Given or Definition ofa linear pair 5. L2 and L3 are supplementary angles 5. Linear pair postulate Definition of supplementary angles Substitution Given or Definition of a linear pair 3. Ll and L2 are supplementary angles 3. Linear pair postulate Definition ofsupplementary angles 5. mll+ml ml4=ml Definition ofcongruent angles Alternate exterior angles converse Page 5 of6,

5 Review Chapter 3: Parallel Lines Name: _ Geometry Date: Period: Part : Classify each statement as true or false.. Two coplanar lines always intersect. _ 2. A transversal is a line which intersects two coplanar lines in two distinct points. 3. Skew lines intersect in one and only one point. _ 4. Sometimes two parallel lines are noncoplanar. _....! \ Part : Use the diagram to answer #5-8. \ k 5. L 3 and L are corresponding angies. \ \ 6. L 3 and L are alternate interior angles. j \... \ 7. How many pairs of corresponding angles are in the diagram? d6 3~ 8. How many pairs of alternate interior angles are in the diagram?,, Part : For #9-6, use the fact that a h,c d and m L 3 =0 0 i ;- c f: 9 (0 c ml7= 0. ml2 = 56 34! d -~ l.mlll= 8(7 6 i 5 2. ml5= a For each pair of congruent angles give, tell which lines you can conclude are parallel. 3. Ll =: L5 4. Ll =:L9 5. L6=:L4 6. L2 =: L6 J b t Part V: Use the following diagram for #7 and #8. 7. f P ~ sand r ~ s, which lines can you conclude are parallel? _ 8. f t ~ q and p q, which lines can you conclude are perpendicular? _ i '--- p ~q '---r-l+... Part v: Use this diagram for #9-27. For each pair of congruent angles given, tell which lines you can conclude are parallel, and state the reason why. 9. L2=: L8 20. L6=:Ll i t 2. Ll=:LlO _ 22. L3 =: L7 _ 23. f ml 6 =2x + 3 and ml = 3x - 6, for what value of x is j k? f f g, j k, m L 2 =40 0 and m L 3 =35 0 then,, 24. ml8= _ 25. ml4= _ 26. ml0= _ 27. ml7= _ Y

6 Part V: Use this diagram for # Given til m, find x. 28. m L 3 = 2x + 6 and m L 5 = 7x - 4. \ 29. m L 4 = 3x + 9 and m L 6 = 2(x + 0) 30. m L 4 = 8x - 80 and m L -2x + 6 Part V: Prove the following. \\ 3. Given: til m, Ll ~ L4 \ "oc "oc Prove: s t 2. Statements Reasons Given: til m, L2 ~ L5 Prove: s t. Statements Reasons ,

7 Review - Chapter 3 Name: Geometry Date: --- Period: --- dentify the pairs of angles as corresponding. alternate Answers interior. alternate exterior. consecutive interior. or vertical angles.. _. L and L8 2. L4 and L5 2. _ 3. L4 and L6 4. L2 and L3 5. L3 and L7 B 7 3. _ 6. L2 and L7 Find the value of x. 4. _ _ _ (3x + 5)0 7. _ 8. _ Find the value of x that makes m n m n 9. _ 0. _. _ 2. _ 3. _ Tell whether the lines through the given points are parallel. perpendicular. or neither. 4. _ 3. Line : (, 2), (2, 0) 4. Line : (-2,), (, -) 5. _ Line 2: (0, -), (-2, -2) Line 2: (,3), (4, ) 6. _ 5. Line : (0, q, (,4) 6. Line : (-, ), (, 3) Line 2: (3,2), (6, 3) Line 2: (2, -), (4, )

8 !.--.' Name _ Date...:. Graph the equation Y = -4x - 8. Y ="2x +"2 Answers - yl J x i )' x r - 9. _ 20. _ 2. _ 22. _ Write an equation of the line that passes through point P and is parallel to the line with the given equation. 23. _ 9. P(-, 3),y = 4x P(2, 4),y = -3x Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. 2. pea, 2),y ="2x P(4, 3), y = -x 23. The graph models the total cost of renting a bike. Write an equation of the line. Explain the meaning of the slope and the y-intercept ofthe line. y - 25 ~.ll! 20 '0 ~ 5 t: 0 o (,) 5 o Bike Rental -.-'./ /'./././ V x Time (hours) -----J 24. _ 25. _ n the diagram, Ai. BC. Find the value of x A c B C

9 : ;; ;; ; ; ::::; z t' Name _ Date _ Vlultiple Choice. Which pair of angles are corresponding angles? 00 L andl8 L3 andl7 L3 andl5 L2andL7 2. What is one way to describe the vertical bars of a football goalpost? 00 perpendicular intersecting skew parallel 3. f two angles lie between two lines and on opposite sides of a transversal, then the angles are _?_. 00 consecutive interior angles alternate interior angles alternate exterior angles corresponding angles 4. Find mll. 6. Find x andy. (4y+ 0)0 (4x+ 4)0 OOx=,y=8 x = 2,y = 8 x = 8,y = x =,y = 2 7. f two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are? 00 intersecting parallel congruent perpendicular 8. What value must x be in order to conclude QR? '

10 9. Describe the slope of the line passing through points A(-2,3) and B(4, negative zero undefined 0. Find the slope of a ladder placed 4 feet from the wall and touching the wall at a height of What is the equation ofthe line through point (2, ) and perpendicular to the line through (-4, ) and (3, y = -~x - ~l y = ~ x _ ~l 2. Write an equation of the line with slope = -2 andy-intercept = -Sx + Sx- y= -2x+ S 3. What best describes the relationship between line 6x - 2y = and line x + 3y = perpendicular skew equivalent ~ FindxifCDJ...FG. F c 30