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NAME ______________________________________________ DATE 4-4 ____________ PERIOD _____ Lesson Reading Guide Proving Congruence—SSS, SAS Get Ready for the Lesson Read the introduction to Lesson 4-4 in your textbook. Why do you think that land surveyors would use congruent right triangles rather than other congruent triangles to check a measurement? Read the Lesson 1. Refer to the figure. N a. Name the sides of 䉭LMN for which ⬔L is the included angle. M b. Name the sides of 䉭LMN for which ⬔N is the included angle. L c. Name the sides of 䉭LMN for which ⬔M is the included angle. 2. Determine whether you have enough information to prove that the two triangles in each figure are congruent. If so, write a congruence statement and name the congruence postulate that you would use. If not, write not possible. b. B E D D C G c. E 苶H 苶 and 苶 DG 苶 bisect each other. d. R G E U F D F S T H Remember What You Learned 3. Find three words that explain what it means to say that two triangles are congruent and that can help you recall the meaning of the SSS Postulate. Chapter 4 28 Glencoe Geometry Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. a. A NAME ______________________________________________ DATE 4-4 ____________ PERIOD _____ Study Guide and Intervention Proving Congruence—SSS, SAS SSS Postulate You know that two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent. The Side-Side-Side (SSS) Postulate lets you show that two triangles are congruent if you know only that the sides of one triangle are congruent to the sides of the second triangle. If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. SSS Postulate Example Write a two-column proof. Given: A 苶B 苶⬵苶 DB 苶 and C is the midpoint of A 苶D 苶. Prove: 䉭ABC ⬵ 䉭DBC B C Statements Reasons 苶B 苶⬵苶 DB 苶 1. A 1. Given 苶D 苶. 2. C is the midpoint of A 2. Given 苶⬵苶 DC 苶 3. 苶 AC 3. Midpoint Theorem 苶⬵苶 BC 苶 4. 苶 BC 4. Reflexive Property of ⬵ 5. 䉭ABC ⬵ 䉭DBC 5. SSS Postulate D Exercises Write a two-column proof. 1. B A C 2. Y Z X T R U S 苶⬵苶 XY 苶, A 苶C 苶⬵苶 XZ 苶, B 苶C 苶⬵苶 YZ 苶 Given: 苶 AB Prove: 䉭ABC ⬵ 䉭XYZ 苶⬵苶 UT 苶, R 苶T 苶⬵苶 US 苶 Given: 苶 RS Prove: 䉭RST ⬵ 䉭UTS Statements Statements Chapter 4 Reasons 29 Reasons Glencoe Geometry Lesson 4-4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. A NAME ______________________________________________ DATE 4-4 Study Guide and Intervention ____________ PERIOD _____ (continued) Proving Congruence—SSS, SAS SAS Postulate Another way to show that two triangles are congruent is to use the Side-Angle-Side (SAS) Postulate. SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Example For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate. a. A b. D X B C Y Z E F In 䉭ABC, the angle is not “included” by the sides 苶 AB 苶 and 苶 AC 苶. So the triangles cannot be proved congruent by the SAS Postulate. H G J The right angles are congruent and they are the included angles for the congruent sides. 䉭DEF ⬵ 䉭JGH by the SAS Postulate. c. P Q 1 2 S R The included angles, ⬔1 and ⬔2, are congruent because they are alternate interior angles for two parallel lines. 䉭PSR ⬵ 䉭RQP by the SAS Postulate. Exercises For each figure, determine which pairs of triangles can be proved congruent by the SAS Postulate. 2. P T 4. Q N U R V 3. N X Y M Z W 5. A W B P L M 6. F G K M Chapter 4 T D C 30 J H Glencoe Geometry Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1.