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Name Class Date Practice 4-1 Form K Congruent Figures Each pair of polygons is congruent. Find the measures of the numbered angles. 1. M 2. Q G B 1 A F 2 1 2 L 90; 40 D 40 N P R C 95 45 60 150 H I 95; 60 Use the diagram at the right for Exercises 3–7. kABC O kXYZ. Complete the congruence statements. u 3. AB > XY X A B Y Z C To start, use the congruence statement to identify the points that correspond to A and B. u u A corresponds to X . B corresponds to Y . u u lY 7. /B > u 5. /Z > lC 4. ZY > CB z 6. /BAC > lYXZ z FOUR O MANY . List each of the following. 8. four pairs of congruent angles lF O lM; lO O lA; lU O lN; lR O lY 9. four pairs of congruent sides FO O MA; OU O AN; UR O NY ; RF O YM For Exercises 10 and 11, can you conclude that the figures are congruent? Justify your answers. 10. nSRT and nPRQ 11. nABC and nFGH S B A R H Q T P No; lSRT O lPRQ because vert. ' are O, and lRST O lRPQ by Third Angles Thm., but none of the sides are necessarily congruent. C G Yes; lBAC O lGFH by Third Angles Thm. Therefore, kABC O kFGH by the def. of O triangles. Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 F Name Class Date Practice (continued) 4-1 Form K Congruent Figures E 12. Given: AD and BE bisect each other. A AB > DE; /A > /D Prove: nACB > nDCE C Statements B Reasons 1) AD and BE bisect each other . AB > DE, /A > /D 1) Given 2) AC > CD, BC > CE 2) 9 Definition of bisect 3) /ACB > /DCE 3) 9 Vertical angles are O. 4) /B > /E 4) 9 Third Angles Theorem 5) nACB > nDCE 5) 9 Definition of O Triangles 13. If nABC > nJKL, which of the following must be a correct congruence statement? C A J B /A > /L /B > /K AB > JL nBAC > nLKJ D K L C 14. Reasoning A student says she can use the information in the figure B C to prove nACB > nACD. Is she correct? Explain. No; explanations may vary. Sample: Corresponding parts are not congruent. The figure can be used to prove kACB O kCAD. A D Algebra Find the values of the variables. 15. nXYZ > nFED 3; 15 Z 30 X 9 in. Y 16. nABD > nCDB 15 D B (5x) (2y) A 75 C D E 3x in. F Algebra kFGH O kQRS. Find the measures of the given angles or the lengths of the given sides. 18. GH 5 3x 2 2; RS 5 x 1 6 10; 10 17. m/F 5 x 1 24; m/Q 5 3x 36; 36 Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 6