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4.3 - Triangle Congruence by ASA and AAS. Postulate 4-3 Angle-Side-Angle (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. UVT XYW.
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Postulate 4-3 Angle-Side-Angle (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. UVT XYW
Theorem 4-2 Angle-Angle-Side (AAS) Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. APX BPY
Which theorem or postulate, if any, could you use to prove that the two triangles are congruent? If possible, write the congruence statement. Not enough information. ASA ∆TVS ∆VTU
Which theorem or postulate, if any, could you use to prove that the two triangles are congruent? If possible, write the congruence statement. AAS ∆WYX ∆AYZ AAS ∆EBC ∆FDC
Which theorem or postulate, if any, could you use to prove that the two triangles are congruent? If possible, write the congruence statement. AAS ∆DEH ∆GEF Not enough information
Given:A R , RA DE Prove: RDE ADE Statements Reasons • _______ • __________ • __________ • __________ • __________ • __________ are rt. angles RDE ADE Use to complete proof: Given, Definition of Perpendicular Lines, Reflexive Property of Congruence, All Right Angles are Congruent, SSS, SAS, ASA, AAS.
Given:A R , RA DE Prove: RDE ADE Statements Reasons • Given • Given • Definition of Perpendicular Lines • All right angles are congruent • Reflexive Property of Congruence • AAS are rt. angles RDE ADE
Given: CE bisects AD, AE || CD Prove: ABE DBC Statements Reasons 1. ___________ 2. ___________ 3. ___________ 4. ___________ 5. ___________ 6. ___________ CE bisects AD AE || CD ABE DBC Use to complete proof: Alternate Interior Angles are Congruent, Given, Definition of Segment Bisector, SSS, SAS, AAS, ASA.
Given: CE bisects AD, AE || CD Prove: ABE DBC Statements Reasons Given Definition of segment bisector Given Alternate Interior Angles are Congruent Alternate Interior Angles are Congruent AAS CE bisects AD AE || CD ABE DBC
Summary: To prove two triangles are congruent, use SSS, SAS, ASA or AAS. (one more later - there are five ways altogether)