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Transcript
Aim: How do we prove triangles congruent using Angle-Side-Angle Postulate? Do Now: In each example, state whether or not the S.A.S. Postulate can be used to prove the triangles congruent. 1) 2) X 3) 4) X Geometry Lesson: A.S.A. Postulate X 1 Postulate: Angle-Side-Angle Postulate (ASA): Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Complete the an triangle by extending the unfinished Construct identical triangle using sides. triangles willincluded be congruent twoThe angles and the side. Ex: Which sides or angles must be proved congruent in order to prove the triangles congruent using the A.S.A Postulate? C A B B 2) 3) 1) E ( B A D C A D C D AC AC 2 AED BEC A C ( Ex 1: Proof w/A.S.A. Given: A D CB bi sec ts AD Prove: ABX DCX A 1 2 X C D Statement 1) 2) 3) 4) 5) 6) A D (a) CB bi sec ts AD at X X is midpoint of AD AX XD (s) 1 2 (a) ABX DCX B Reason 1) 2) 3) 4) 5) Given Given Def. line bisector Def. midpoint Vertical angles are congruent. 6) A.S.A. Postulate Geometry Lesson: A.S.A. Postulate 3 A Ex 2,3,4: Proofs w/A.S.A. 2) Given: ADE BDC, E C D is midpoint of EC Prove: ADE BDC E 3) Given: AC bisects EB at D AE EB, CB EB Prove: AED CBD B C D A B E D B 4) Given: BP AC BP bisects ABC Prove: ABP CBP A Geometry Lesson: A.S.A. Postulate P C C 4 A Ex 5,6: Proofs w/A.S.A. 5) Given: BCDE , ACB FDE B E , BD EC B Prove: CBA DEF C D Geometry Lesson: A.S.A. Postulate E D A 6) Given: DB bisects ABC DB bisects ADC Prove: ABD CBD F B C 5