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9. A flow proof uses figures in the coordinate plane and algebra to prove geometric concepts. ANSWER: false; coordinate proof Study Guide and Review State whether each sentence is true or false . If false , replace the underlined word or phrase to make a true sentence. 1. An equiangular triangle is also an example of an acute triangle. 10. The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. ANSWER: true ANSWER: true Classify each triangle as acute, equiangular, obtuse, or right. 2. A triangle with an angle that measures greater than 90° is a right triangle. ANSWER: false; obtuse 3. An equilateral triangle is always equiangular. 11. ANSWER: true ANSWER: obtuse 4. A scalene triangle has at least two congruent sides. ANSWER: false; isosceles 5. The vertex angles of an isosceles triangle are congruent. 12. ANSWER: right 13. ANSWER: false; base ANSWER: right 6. An included side is the side located between two consecutive angles of a polygon. ALGEBRA Find x and the measures of the unknown sides of each triangle. ANSWER: true 7. The three types of congruence transformations are rotation, reflection, and translation. 14. ANSWER: true ANSWER: x = 12, RS = RT = 31 8. A rotation moves all points of a figure the same distance and in the same direction. ANSWER: false; translation 9. A flow proof uses figures in the coordinate plane and algebra to prove geometric concepts. ANSWER: false; coordinate proof 10. The measure of an exterior angle of a triangle is of its two remote interior angles. eSolutions equalManual to the- Powered sum of by theCognero measures ANSWER: 15. ANSWER: x = 6, JK = KL = JL = 24 16. MAPS The distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles. ThePage 1 distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago, and the 15. ANSWER: Study Guide and Review x = 6, JK = KL = JL = 24 ANSWER: 104 Show that the polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement. 16. MAPS The distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles. The distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago, and the distance from Cleveland to Cincinnati is 50 miles less than the distance from Cincinnati to Chicago. Find each distance and classify the triangle formed by the three cities. ANSWER: Cin. to Chi. = 300 miles, Cin. to Clev. = 250, Chi. to Clev. = 350; scalene 21. ANSWER: D J, A F, C H, Find the measure of each numbered angle. ABCD 17. 2 ANSWER: 110 19. polygon FGHJ 1 ANSWER: 70 18. B G, polygon 3 22. ANSWER: X J, Y K, Z L, 23. MOSAIC TILING A section of a mosaic tiling is s triangles that appear to be congruent. ANSWER: 82 20. HOUSES The roof support on Lamar’s house is in the shape of an isosceles triangle with base angles of 38°. Find x. ANSWER: Determine whether Explain. 24. A(5, 2), B(1, 5), C(0, 0), X(–3, 3), Y(–7, 6), Z(–8, 1) ANSWER: ANSWER: 104 Show that the polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement. eSolutions Manual - Powered by Cognero 21. Yes, by SSS. AB = XY = 5, BC = YZ = ZX = CA= 25. A(3, –1), B(3, 7), C(7, 7), X(–7, 0), Y(–7, 4), Z(1, 4) ANSWER: No, the corresponding sides of the two triangles are not congruent. Determine which postulate can be used to Page 2 prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. 25. A(3, –1), B(3, 7), C(7, 7), X(–7, 0), Y(–7, 4), Z(1, 4) ANSWER: No, the corresponding Study Guide and Review sides of the two triangles are not congruent. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. ANSWER: The triangles are congruent by SAS. Write a two-column proof. 29. Given: Prove: 26. ANSWER: SAS ANSWER: Statements (Reasons) 1. (Given) 2. A DCE (Alternate Interior 3. (Given) 4. ABE D (Alternate Interior 5. (ASA) 27. ANSWER: not possible 28. PARKS The diagram shows a park in the shape of a pentagon with five sidewalks of equal length leading to a central point. If all the angles at the central point have the same measure, how could you prove that s Thm.) s Thm.) 30. KITES Denise’s kite is shown in the figure below. Given that bisects both XWZ and XYZ, prove that ANSWER: Statements (Reasons) 1. bisects both XWY and XZY. (Given) 2. XWY ZWY (Def. of Bisector) 3. (Reflexive Property) 4. XYW ZYW (Def. of Bisector) 5. (ASA) ANSWER: The triangles are congruent by SAS. Write a two-column proof. 29. Given: Prove: Find the value of each variable. ANSWER: Statements (Reasons) 1. (Given) eSolutions Manual - Powered by Cognero 2. A DCE (Alternate Interior 3. (Given) 31. ANSWER: 3 s Thm.) Page 3 1. bisects both XWY and XZY. (Given) 2. XWY ZWY (Def. of Bisector) 3. (Reflexive Property) 4. Guide XYWand Review ZYW (Def. of Bisector) Study 5. (ASA) Find the value of each variable. 31. ANSWER: 3 32. ANSWER: 76 33. PAINTING Pam is painting using a wooden easel. The support bar on the easel forms an isosceles triangle with the two front supports. According to the figure below, what are the measures of the base angles of the triangle? ANSWER: 77.5 eSolutions Manual - Powered by Cognero Page 4