Name Class Date. Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed.

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1 hapter 9 Parallel Lines 79 hapter 9- Proving Lines Parallel Version [20 points] hapter 9-2 Properties of Parallel Lines PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2] In 2, use the figure given below.. If m 2x 40 and m 4 4x 0, find the value of x so that y. () 0 (2) 25 (3) 45 (4) If m 2 x and m 3 3x 2, find the value of x so that y. () 40 (2) 48 (3) 52 (4) In the given figure, l m. Find the measure of x. () 05 (2) 0 (3) 35 (4) x F 2 r l m 4. Given: l m and r is a transversal. If c 03, what is the value of a b? () 54 (3) 80 (2) 77 (4) In the given figure, if m m 2, what is the value of x? 35 m 3 () 50 (3) 05 (2) 75 (4) In the given figure, if m m 2 and a b, which of the following statements is not true? () m 2 m 3 (2) m m 3 a b r 40 cd x a b m (3) line parallel to m must be perpendicular to m 3. (4) line that intersects m must also intersect m 2. l m m 2 m 4 m m 3 m 2

2 80 hapter 9 Parallel Lines PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. a. In the given figure, c d and lines a and b are transversals with line a bisecting QRS. If m x 48, what is m y? b a S 24 nswer: m y 24 Q 24 R x y c d 24 b. In the given figure, m 00, m FG 30, y, and y FG. Find m. nswer: m F G 8. Given: >,m 6 m 3 Prove: l m l Proof: m Statements Reasons. >. Given Isosceles triangle theorem. 3. m 7 m 6 3. efinition of congruent angles. 4. m 6 m 3 4. Given. 5. m 7 m 3 5. Transitive property efinition of congruent angles. 7. l m 7. If two coplanar lines are cut by a transversal so that the corresponding angles are, then the two lines are.

3 hapter 9 Parallel Lines 8 hapter 9- Proving Lines Parallel Version [20 points] hapter 9-2 Properties of Parallel Lines PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2]. In the given figure, which information would not guarantee that two lines are parallel? 4. In the figure given, if l m, what is the measure of x? d () 4 (2) 3 5 (3) 2 4 (4) a d and b d In the given figure, if g r and b 93, what is the value of c d? () 73 (3) 75 (2) 74 (4) 80 a s c c b 3. If lines m and n are parallel and are intersected by transversal y, what is the sum of the measures of the interior angles on the same side of line y? () 90 (2) 80 (3) 270 (4) d 4 a b g r () 5 (3) 45 (2) 30 (4) In the figure given, lines m and p are parallel and bisects. What is the measure of x? m p x () 55 (3) 65 (2) 60 (4) In the given figure, lines a and b are not parallel. Which of the following could not be the value of x? 03 x () 76 (3) 78 (2) 77 (4) 79 x c 2x n 0 a l b m

4 82 hapter 9 Parallel Lines PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. a. In the given figure, g y g, ', m 2x, and m 3x. Find the value of x. 3x nswer: x 8 lternate interior angles formed by cutting parallel lines are congruent, so m 2x. 2x 2x 3x x 5 90 x 5 8 b. In the given figure, y, y F, m 33, and m 58. Find m F. nswer: m F 89 orresponding angles formed by cutting parallel lines are congruent, so m F 33 and m F 58. F m/f 5 80 m/f Given: 3 and 2 3 Prove: G g y H g 3 2 F Proof: G H Statements Reasons Given. 2. g y g 2. If two coplanar lines are cut by a transversal so that the corresponding angles are, then the two lines are Given Transitive property. 5. G g y H g 5. If two coplanar lines are cut by a transversal so that the corresponding angles are, then the two lines are.

5 hapter 9 Parallel Lines 83 hapter 9-3 Parallel Lines in the oordinate Plane Section Quiz [20 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2]. If g y g and the slope of g is, then the slope of g 2 is () 2 (2) 2 2 (3) 2 (4) 2 2. Find the equation of the line through (, 2) and parallel to the line with equation y 7x 2. () y 2 7 x (2) y 2 7 x 5 7 (3) y 7x 9 (4) y 7x 9 3. Which is the equation of the line that is parallel to the x-axis and passes through the point (, 4)? () x (2) y (3) x 4 (4) y 4 4. Which is the equation of a line passing through (2, 5) and parallel to the line whose equation is y 3x 2? () y 3x (2) y 3x 5 (3) y x 7 (4) y 3x 5. What is the slope of a line parallel to if ( 4, 3) and (7, )? () (2) (3) (4) 6. The lines x 2y 5 and 4x + ky 5 are parallel for which value of k? () 4 (2) (3) 2 2 (4)

6 84 hapter 9 Parallel Lines PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. The coordinates of quadrilateral are ( 5, 4), (, 2), (2, 3), and ( 4, ). Show that both pairs of opposite sides are parallel. The slopes of opposite sides are equal: Slope of 5 Slope of 22 2 (24) 2 (25) (24) Slope of Slope of (22) (24) 24 2 (25) Trapezoid PQRS has parallel bases PQ and SR. The coordinates of the vertices are P(0, 0), Q(k, 5), R(7, ), and S(k, 3). a. xpress the slope of PQ in terms of k. 5 nswer: k b. xpress the slope of SR in terms of k nswer: k 2 7 or 7 2 k c. Write an equation that can be used to solve for k and solve this equation for k. 5 k k 2k 5 5(7 2 k) 2k k 7k 5 35 k 5 5 nswer

7 hapter 9 Parallel Lines 85 hapter 9-4 The Sum of the Measures of the ngles of a Triangle Section Quiz [20 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2]. If the measure of the angles of a triangle are in the ratio 3 : 5 : 7, then what is the measure of the largest angle? () 36 (2) 60 (3) 84 (4) In the given figure, two angle measures are shown. 44 What is the value of x? () 36 (2) 82 (3) 98 (4) 02 x In triangle, the measure of is twice the measure of, and an exterior angle at vertex measures 7. What is the measure of? () 39 (2) 78 (3) 02 (4) 7 4. In the given figure, l m,m 49, bisects, and bisects. Find the value of x. () 49 (3) 90 (2) 82 (4) If the degree measures of three angles of a triangle are represented by x 20, 5x 50, and 9x 40, the triangle must be () right (2) isosceles (3) acute (4) scalene 6. In the given figure, l m,m 30, m 25, and is a right triangle. x What is the measure of x? () 25 (3) 05 (2) 65 (4) 55 x l m l m

8 86 hapter 9 Parallel Lines PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. In the given figure, m 45, m 35, and y. Find the degree measures of the angles numbered to 6. nswer: m 80, m 2 00, m 3 80, m 4 35, m 5 00, m 6 45 Since y, and 6 are congruent corresponding angles. Therefore, m 6 m 45. The sum of the degree measures in a triangle is 80, so: m/ m/6 m/ and 2, 3 and 5, and 4 and 6 form linear pairs, so: m/ m/ m/ m/ In RST, the bisectors of the angles meet at point P. If m RTS 60, m RPT 25, and m RPS 20, find the degree measures of the angles numbered to 4. nswer: m 5, m 2 35, m 3 35, m 4 25 TP bisects RTS, so m RTP m STP 2 (60) 30. The sum of the degree measures in a triangle is 80, so: RP bisects TRS, so m SRP m SP bisects RST, so m 2 m m/ m/ m/3 m/ m/ m/ m/rtp m/rpt m/ m/ m/ m/srp m/rps m/ m/ m/ m/ m/2 m/stp 5 80 m/ m/ m/ m/ m/ m/ m/ m/4 m/ m/ m/ R S 3 2 P F T

9 hapter 9 Parallel Lines 87 hapter 9-5 Proving Triangles ongruent by ngle, ngle, Side Section Quiz [20 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [6] g. In the figure given, F ' and a b. G F 2. Which of the following pairs of triangles can not be proved congruent by S? () (3) a b (2) (4) Which additional information would permit you to prove that F FG by the S theorem? () G (2) F GF (3) F > GF (4) > G 3. Given: lies on the angle bisector of. Which of the following statements is true? () If ' h, then. (2) If ' h, then. (3) If ' h and ' h, then. (4) If, then ' h and ' h.

10 88 hapter 9 Parallel Lines PRT II nswer all questions in this part. ach correct answer will receive credit. No partial credit will be allowed. [6] 4. omplete the proof by filling in the missing reasons. Given: >, M ', MF ', and M is the midpoint of. F Prove: M > MF Proof: M Statements Reasons. >. Given Isosceles triangle theorem. 3. M ' and MF ' 3. Given. 4. M and MF are right angles. 4. efinition of perpendicular lines. 5. M MF 5. Right angles are congruent. 6. M is the midpoint of. 6. Given. 7. M > M 7. efinition of midpoint. 8. M FM 8. S (steps 2, 5, 7). 9. M > MF 9. orresponding parts of congruent triangles

11 hapter 9 Parallel Lines 89 PRT III nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 5. Given: ', ', and 2 Prove: Proof: Statements Reasons. ' and '. Given. 2. and are right angles. 2. efinition of perpendicular lines Right angles are congruent. 4. > 4. Reflexive property Given. 6. and 3 are supplements. 6. efinition of supplementary angles. 2 and 4 are supplements If two angles are, then their supplements are S. 6. Given: F, F ', ', 2, F >. Prove: F 2 Proof: F Statements Reasons. F ' and '. Given. 2. F and are right angles. 2. efinition of perpendicular lines. 3. F 3. Right angles are congruent Given. 5. F > 5. Given. 6. F F > F 6. ddition postulate F F 7. Partition postulate. F 5 F 8. > F 8. Substitution postulate. 9. F 9. S.

12 90 hapter 9 Parallel Lines hapter 9-6 The onverse of the Isosceles Triangle Theorem Section Quiz [20 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2]. The measure of each base angle of an isosceles triangle is 5 degrees more than the measure of the vertex angle. What is the measure of the vertex angle? () 50 (3) 30 (2) 40 (4) The measure of vertex angle L of an isosceles triangle is three times the measure of each of the base angles, M and N. Which of the following statements is true? () MN 2LM (3) LM LN MN (2) LM LN MN (4) 4LM 4LN 3. In isosceles,m 40. Which statement can not be true? () and (2) m m (3) m 00 (4) 4. In PQR,m P x 37, m Q 3x 67, and m R = 4 x 2. For the triangle to be isosceles, which of the following must be the value of x? () 64 (3) 52 (2) 20 4 (4) If the degree measures of the three angles of a triangle are represented by x 25, 3x 5, and 4x 0, which of the following choices most completely describes the triangle? () scalene and right (2) isosceles and right (3) isosceles and acute (4) equilateral and equiangular 6. In each of the following, two angle measures of a triangle are given. Which of these could not be the angles of an isosceles triangle? () 70, 40 (3) 80, 20 (2) 30, 20 (4) 35, 65 PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. a. ach of the congruent angles of an isosceles triangle measures 8 degrees less than 4 times the vertex angle. Find: () the measure of the vertex angle. nswer: 24 Let the measure of the vertex angle x. Then each base angle measures 4x 8. 4x 2 8 4x 2 8 x x 5 26 x 5 24

13 hapter 9 Parallel Lines 9 (2) the measure of the base angles. 4(24) 8 78 nswer b. In,. If 5x 7 and 2x, find: () the value of x. 5x x 3x 5 8 (2) the lengths of and. nswer: 23 5(6) 7 23 x 5 6 nswer 8. Given: QR, QRS, RT h bisects SR, RT h y Q Prove: a. QR > R b. QR is isosceles. R S 2 T Proof: Q Statements Reasons a.. RT h bisects SR.. Given efinition of angle bisector. 3. RT h y Q 3. Given. 4. Q 4. If two parallel lines are cut by a transversal, then the corresponding angles are If two parallel lines are cut by a transversal, then the alternate interior angles formed are. 6. Q 6. Transitive property. 7. QR > R 7. onverse of the isosceles triangle theorem. b. 8. QR is isosceles. 8. Isosceles triangle theorem.

14 92 hapter 9 Parallel Lines hapter 9-7 Proving Right Triangles ongruent by Hypotenuse-Leg Section Quiz [20 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2]. 4. In right triangle, angle bisectors M, R, and U are drawn and intersect at point X. U M R X U T To prove UTM by the hypotenuse-leg theorem, which additional corresponding parts must be congruent? () and UT (3) and U (2) and UM (4) and M 2. In the given figure, is the midpoint of, ', ', and >. 5. M Which statement must be true? () m RX 45 (3) M (2) m RX 45 (4) M O Which method of proof may be used to prove? () SS (3) HL (2) H (4) S 3. Two right triangles are not necessarily congruent if () the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle. (2) the hypotenuse and an acute angle of one triangle are congruent to the corresponding parts of the other triangle. (3) the corresponding acute angles of the triangles are congruent. (4) two legs of one triangle are congruent to two legs of the other triangle. Which of the following is not sufficient to show that O O? () ', ', O is the midpoint of, and >. (2) ', O is the midpoint of, and >. (3) ', ', and >. (4) ', ', and O is the midpoint of. 6. Which of the following statements is true? () HL can never be used to prove isosceles triangles congruent. (2) HL can never be used to prove acute triangles congruent. (3) HL is a special case of SS. (4) HL is a special case of S.

15 hapter 9 Parallel Lines 93 PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. Given: In, is a right angle, ', and >. Prove: Proof: Statements Reasons. is a right angle, ',. Given. and >. 2. is a right angle. 2. efinition of perpendicular lines. 3. > 3. Reflexive property HL. 8. Given: M ', ', M >, and >. Prove: > M M Proof: Statements Reasons. M ', '. Given. 2. M and are right angles. 2. efinition of perpendicular lines. 3. M >, > 3. Given. 4. M M > M 4. ddition postulate M M, M 5 M 5. Partition postulate. 6. > M 6. Substitution postulate. 7. M 7. HL. 8. > M 8. orresponding parts of congruent triangles are.

16 94 hapter 9 Parallel Lines hapter 9-8 Interior and xterior ngles of Polygons Section Quiz [20 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [2]. If the measures of the exterior angles at any two vertices of a triangle are equal, which of the following is false? () The triangle is equiangular. (2) The triangle is equilateral. (3) The triangle is concave. (4) The triangle is convex. 2. If the sum of the measures of the exterior angles of hexagon F is 360, which of the following must be true? () ll exterior angles of F are congruent. (2) ll interior angles of F are congruent. (3) F is a regular polygon. (4) none of the above 3. If each exterior angle of a regular polygon contains 45, how many sides does it have? () 6 (3) 8 (2) 7 (4) 9 4. What is the measure of one exterior angle of a regular pentagon? () 72 (3) 360 (2) 08 (4) The sum of the measures of the interior angles of a certain convex polygon is 720. The sum of the measures of the interior angles of a second convex polygon that has two more sides than the first is () 720 (2) 900 (3),080 (4), The greatest measure that an exterior angle of any regular polygon can have is () 60 (3) 90 (2) 72 (4) 20 PRT II nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8] 7. a. If the sum of the measures of eight interior angles of a nonagon is,80, what is the measure of the ninth angle? nswer: 80 The sum of the measures of the interior angles of a nonagon is: 80(9 2),260 The ninth angle measures,260,80 80.

17 hapter 9 Parallel Lines 95 b. The measure of each exterior angle of a regular decagon is x 8. Find the value of x and the measure of each exterior angle. nswer: x 28, exterior angle 36 decagon has 0 sides. 360 ach exterior angle measures x x a. How many sides does a polygon have if the sum of the interior angles is four times the sum of the measures of its exterior angles? nswer: 0 sides The sum of the exterior angles 360. Then the sum of the interior angles 4(360), (n 2 2) 5,440 n n 5 0 b. If an exterior angle of a regular polygon measures 3x and an interior angle measures 6x, how many sides does the polygon have? What is the name of the polygon? nswer: 6 sides, hexagon 80(n 2 2) Since each interior angle measures 6x, n 5 6x Since each exterior measures 3x, n 5 3x or n 5 6x. 80(n 2 2) n n 80(n 2 2) n n 5 6

18 96 hapter 9 Parallel Lines hapter 9 Parallel Lines hapter Review [40 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [6]. In the given figure, m x and p m. m p c a b x 4. In, if >, m x 0 and m 2x 20, what is the degree measure of? () 30 (2) 40 (3) 00 (4) 20 Which of the following must be false? () x p (2) m p (3) m a m b (4) m c m b 2. If the coordinates of are ( 3, 4), (4, 5), and (4, 5), what is the slope of a line parallel to the line that passes through? () (3) 7 (2) (4) 7 3. In the given figure, r s and lines l and m are transversals. What is value of x? () 35 (3) 60 (2) 45 (4) 75 l m x r s 5. ach interior angle of a regular polygon has a measure of 40. How many sides does the polygon have? () 8 (3) 0 (2) 9 (4) 6. n exterior angle at the base of an isosceles triangle is always () acute (2) right (3) obtuse (4) cannot be determined 7. If the degree measures of the three angles of a triangle are represented by x 30, 4x 30, and 0x 30, which of the following choices most completely describes the triangle? () scalene and right (2) isosceles and right (3) isosceles and acute (4) equilateral and equiangular 8. What is the measure of one interior angle of a regular octagon? () 08 (3) 35 (2) 20 (4) 44

19 hapter 9 Parallel Lines 97 PRT II nswer all questions in this part. ach correct answer will receive 2 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [4] g 9. In the given figure, parallel lines g and are intersected by transversal F g at points G and H, respectively. If m G x 40 and m GH 4x 50, what is the value of x? nswer: 38 G F x 40 4x H 5x x 5 90 x In the given figure, y, g y g, and m m 2. Find the measures of x and y. nswer: m x 50, m y 65 m m y (lternate interior angles) m y m 2 (Substitution postulate) m m F 30 (orresponding angles) y the partition postulate: m/y m/ m/y 5 30 m/y 5 65 m/x m/2 m/y 5 80 m/x m/x 5 50 x y 2 30

20 98 hapter 9 Parallel Lines PRT III nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8]. Line l is parallel to line m, and lines r and s are transversals. If, what is m? nswer: m 00 m (Supplementary angles) m m 40 (ase angles of an isosceles triangle) m m 40 (Vertical angles) m m 40 (lternate interior angles) m 80 m m (Sum of the angle measures in a triangle) r s 40 l m 2. Isosceles with >, m 4x 5, and m x 23. a. Find m. nswer: m 38 4x 5 5 x x x 5 4 m/ 5 m/ 5 4(4) m/ b. True or False?. Justify your answer. nswer: False xplanation: If the measures of two angles of a triangle are unequal, then the lengths of the sides opposite these angles are unequal with the longer side opposite the larger angle., so.

21 hapter 9 Parallel Lines 99 PRT IV nswer all questions in this part. ach correct answer will receive 6 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [2] 3. The vertices of are ( 2, 0), (6, 0), and (8, 6). a. Write an equation of the line through point parallel to. nswer: y 3x 6 Slope of y 5 3x b 0 5 3(22) b 6 5 b Therefore, the equation of the line is y 3x 6. b. Write an equation of a line through point parallel to. nswer: y 6 Slope of (22) 5 0 c. The lines whose equations were found in parts a and b intersect in point. Find the coordinates of. nswer: (0, 6) 3x x 5 0 x 5 0 y 5 3(0) 6 5 6

22 200 hapter 9 Parallel Lines 4. Given: H and are altitudes of and 2. Prove: is isosceles. H Proof: 2 Statements Reasons. H and are altitudes of.. Given. 2. H ' and ' 2. efinition of altitude. 3. H and are right angles. 3. efinition of perpendicular lines. 4. H 4. Right angles are congruent Given. 6. > 6. Reflexive property. 7. H 7. S. 8. H 8. orresponding parts of congruent triangles are. 9. > 9. onverse of the isosceles triangle theorem. 0. is isosceles. 0. efinition of isosceles triangle.

23 hapter 9 Parallel Lines 20 hapter 9 Parallel Lines umulative Review [40 points] PRT I nswer all questions in this part. ach correct answer will receive 2 credits. No partial credit will be allowed. [6]. If the unequal sides of a triangle are 3, x, and 7, then what is the smallest integer value of x? () 3 (3) 5 (2) 4 (4) 6 2. Given: MP with Q a perpendicular bisector of MP MQ is congruent to PQ by which of the following reasons? () SSS (3) S (2) SS (4) HL 3. In the given figure, if point P is the same distance from the origin as point M, which of the following could be the coordinates of point P? M(a, b) () ( a, b) (3) ( b, a) (2) (a, b) (4) ( b, a) 4. Which of the following statements is true? () very acute triangle is scalene. (2) Some right triangles are obtuse. (3) No scalene triangle is isosceles. (4) Some obtuse triangles are equilateral. P O y x 5. What is the slope of the line with the equation 3(x ) 4y 0? () 0.75 (2) 0.75 (3) 3 (4) 4 6. If ~ and are true, then which of the following is also true? () ~ (2) ~ (3) (4) cannot be determined 7. Under the transformation r y-axis + R 908, the image of (5, 2) is () (2, 5) (2) (2, 5) (3) ( 2, 5) (4) ( 2, 5) 8. What are the coordinates of the midpoint of the line segment with endpoints at (a, b) and (g, h)? () (g a, h b) (2) g 2 a 2, h 2 2 b (3) (g a, h b) (4) g a 2, h b 2

24 202 hapter 9 Parallel Lines PRT II nswer all questions in this part. ach correct answer will receive 2 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [4] 9. Find the sum of the measures of the interior angles of a 22-sided polygon. 80(22 2) 3,600 nswer 0. In the given figure, what is the average measure of the angles marked, 2, and 3? nswer: 60 xplanation: ach angle marked is a vertical angle with an angle of a triangle. The sum of the 80 measures of the angles of a triangle is 80, so the average is PRT III nswer all questions in this part. ach correct answer will receive 4 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [8]. Find the equation of the perpendicular bisector of the line segment with endpoints ( 3, 5) and (, 3). nswer: y 52 2 x , Midpoint of the given segment 3 2 (25) Slope of given segment 2 (23) Slope of perpendicular line 2 2 (, ) y 52 2 x b (2) b b Therefore, the equation of the perpendicular bisector is y 52 2 x

25 hapter 9 Parallel Lines The coordinates of F are ( 2, ), (2, 7), and F(6, 0). Under a translation the image of is (, 3). a. If the translation can be written as (x, y) (x a, y b), what are the values of a and b? nswer: a, b 2 Since ( 2, ) (, 3), the translation is defined by (x, y 2). b. Find the coordinates of and F. nswer: (3, 9), F (7, 2) T, 2 (2, 7) (3, 9) T, 2 (6, 0) (7, 2) PRT IV nswer all questions in this part. ach correct answer will receive 6 credits. learly indicate the necessary steps, answer with no work shown will receive only credit. [2] 3. In, 2x 3, 3x, and 4x 2. The perimeter of is 36. a. Find the value of x. b. Find the length of each side. nswer:,, 4 5 2x 3 5 2(4) 3 5 c. Name the largest angle or angles. nswer: 2x 3 3x 2 4x x 2 5 3(4) 2 5 9x 5 36 x 5 4 nswer 5 4x (4)

26 204 hapter 9 Parallel Lines 4. Given:, >, G > R, G ', R ' Prove: G > R G R Proof: Statements Reasons. >, G > R. Given Isosceles triangle theorem. 3. G ', R ' 3. Given. 4. G and R are right angles. 4. efinition of perpendicular lines. 5. G R 5. Right angles are congruent. 6. G R 6. S. 7. G > R 7. orresponding parts of congruent triangles are.