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Name ——————————————————————— Practice A LESSON 4.4 LESSON 4.4 Date ———————————— For use with pages 250–257 Use the diagram to name the included angle between the given pair of sides. } } 1. GH and HI } } } } } } } } H 2. HI and IG 3. IG and HG I G 4. GI and IJ 5. JG and IG } } 6. IJ and GJ J Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. 8. n ABD, n CBD M L A O N D P 9. n DEG, n FGE B 10. n RST, n VUT F U V E T G D S 250 Geometry Chapter 4 Resource Book C R Copyright © Holt McDougal. All rights reserved. 7. n LMN, n NOP Name ——————————————————————— Practice A LESSON 4.4 For use with pages 250–257 Date ———————————— continued 11. n HIJ, n HKJ 12. n WXY, n WZY X I W Y J H LESSON 4.4 Decide whether enough information is given to prove that the triangles are congruent using the HL Congruence Theorem. Z K State the third congruence that must be given to prove that n ABC > n DEF using the indicated postulate or theorem. } } 13. GIVEN: ∠ B ù ∠ E, BC ù EF, ? ù ? Use the SAS Congruence Postulate. } } } } 14. GIVEN: AB ù DE, BC ù EF, ? ù ? Use the SSS Congruence Postulate. } } 15. GIVEN: AC ù DF, ∠ A is a right angle and ∠ A ù ∠ D, ? ù ? B A E C D F Copyright © Holt McDougal. All rights reserved. Use the HL Congruence Theorem. 16. Skateboards Suppose you have two skateboard ramps. What information do you need to know to prove that the triangular ramps are congruent using SAS? using HL? Geometry Chapter 4 Resource Book 251 Lesson 4.3, continued Statements } } 6. AF > EC 7. n AFB > n CEB 4. Copyright © Holt McDougal. All rights reserved. Statements 1. n ZWV > n YXV } } 2. ZW > YX } } VZ > VY } } WV > XV 3. WV 1 VY 5 WY XV 1 VZ 5 XZ 4. WV 5 XV; VZ 5 VY Reasons 1. Given 2. Definition of congruent triangles 3. Segment Addition Postulate 4. Definition of Congruent Segments 5. XV 1 VZ 5 WY 5. Substitution property of equality 6. WY 5 XZ 6. Substitution property of equality } } 7. Definition of 7. WY > XZ congruent segments } } 8. Reflexive prop. of 8. ZY > ZY congruence 9. n ZWY > n YXZ 9. SSS Congruence Postulate 5. The diagram shows two equilateral triangles, n ABC and n DEF. If one side of n ABC is congruent to one side of n DEF, such as } } AB > DE, then you know that the triangles are congruent because equilateral triangles have three E B congruent sides. A C D F 6. J(3, 9), K(7, 8) Lesson 4.4 1. ∠ ABC 2. ∠ BCD 3. ∠ ABD 4. ∠ BDA 5. ∠ DAB 6. ∠ CDB 7. not enough 8. enough 9. not enough 10. Yes, SAS Congruence Postulate 11. Yes, HL Congruence Theorem } } 12. not enough 13. RM ù FB 14. ∠ J ù ∠ D } } } } } } 15. JM ù DB or JR ù DF 16. Given; AB ù BE; } } Given; CB ù BD; Vertical Angles Theorem; SAS Congruence Postulate 17. Given; Alternate Interior Angles Theorem; Given; Reflexive Property of Congruence; SAS Congruence Postulate Practice Level C 1. not enough 2. enough; HL 3. not enough } } 4. enough; SAS 5. ∠ BCA; ∠ EDF 6. BC; ED } } 7. AC; FD 8. They are congruent by SAS. 9. Definition of perpendicular lines; n PRS and n QSR are right triangles; Reflexive Property of Congruence; HL Congruence Theorem 10. ∠ OML and ∠ OMN are right angles; ∠ OML ù ∠ OMN; Given; Reflexive Property of Congruence; SAS Congruence Postulate Review for Mastery 1. Yes; You are given that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. 2. Yes; ∠ JKN and ∠ MKL are congruent because they are vertical angles. So you have two sides and the included angle of one triangle that are congruent to two sides and the included angle of another triangle. 3. No; You have two sides in nWXY that are congruent to two sides in n ZXY, but the angle in n ZXY is not the included angle. 4. Practice Level A 1. ∠ GHI Practice Level B ANSWERS Reasons 6. Definition of congruent segments 7. SSS Congruence Postulate 2. ∠ HIG 3. ∠ IGH 4. ∠ GIJ 5. ∠ JGI 6. ∠ IJG 7. enough 8. not enough 9. enough 10. not enough 11. enough } } } } 12. not enough 13. AB; DE 14. AC; DF } } 15. BC; EF 16. Two sides and the included angle of one ramp need to be congruent to the corresponding sides and angle of the second ramp; the two ramps need to be right triangles with congruent hypotenuses and one pair of congruent corresponding legs. Statements } } H 1. AB > DB } } 2. BC ⊥ AD 3. ∠ ACB and ∠ DCB are right angles. 4. n ABC and n DCB are right triangles. } } L 5. BC > BC 6. n ABC > n DBC Reasons 1. Given 2. Given 3. Def. of ⊥ lines 4. Def. of a right triangle 5. Reflexive Property of Congruence 6. HL Congruence Theorem Geometry Chapter 4 Resource Book A45