Transcription of NAME DATE PERIOD 4-4 Study Guide and Intervention
1 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, DATE PERIOD Lesson 4-4 Chapter 4 25 Glencoe GeometryStudy Guide and InterventionProving Triangles Congruent SSS, SASSSS 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.
2 Write a two-column proof. Given: AB DB and C is the midpoint of AD .Prove: ABC DBC BCDAS tatements Reasons1. AB DB 1. Given2. C is the midpoint of AD . 2. Given3. AC DC 3. Midpoint Theorem4. BC BC 4. Reflexive Property of 5. ABC DBC 5. SSS PostulateExercisesWrite a two-column proof. 1. BYCAXZG iven:AB XY , AC XZ , BC YZ Prove: ABC XYZ 2. TURSG iven: RS UT , RT US Prove: RST UTS4-4 SSS PostulateIf three sides of one triangle are congruent to three sides of a second triangle, then the triangles are ReasonsStatements Reasons1.
3 AB XY 1. Given AC XZ BC YZ 2. ABC XYZ 2. SSS RS UT 1. Given RT US 2. ST TS 2. Refl. RST UTS 3. SSS Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, DATE PERIOD Chapter 4 26 Glencoe GeometryStudy Guide and Intervention (continued)Proving Triangles Congruent SSS, SASSAS Postulate Another way to show that two triangles are congruent is to use the Side-Angle-Side (SAS) Postulate.
4 For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate. a. ABCXYZ b. DHFEGJ c. PQS12R In ABC, the angle is not The right angles are The included angles, included by the sides AB congruent and they are the 1 and 2, are congruent and AC . So the triangles included angles for the because they are cannot be proved congruent congruent sides. alternate interior angles by the SAS Postulate. DEF JGH by the for two parallel lines.
5 SAS Postulate. PSR RQP by the SAS PostulateIf two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
6 Then the triangles are the specified type of proof. 1. Write a two column proof. 2. Write a two-column proof. Given: NP = PM, NP PL Given: AB = CD, AB CD Prove: NPL MPL Prove: ACD CABP roof: Proof: 3. Write a paragraph : V is the midpoint of YZ . V is the midpoint of WX .Prove: XVZ WVY Since V is the midpoint of YZ and the midpoint of WX , by the definition of midpoint, YV = VZ and WV = VX.
7 Since YVW and XVZ are vertical angles, by the Vertical Angle Theorem the angles are congruent. Therefore, by SAS, XVZ "%$#8:7;9 StatementsReasons1. NP = PM, NP PL 2. MPL is a right angle; NPL is a right MPL NPL4. PL PL 5. NPL MPL1. Given2. Perpendicular lines form right All right angles are Reflexive Property of Congruence5. SASS tatementsReasons1. AB = CD, AB CD 2. BAC DCA 3. AC = AC4. ACD CAB1. Given2. Alternate Interior Angles Theorem3. Reflexive Property of Congruence4.
8 SAS
