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4.5 – Prove Triangles Congruent by ASA and AAS. Angle-Side-Angle (ASA) Congruence Postulate. E. F. 4 cm. B. C. 4 cm. D. A.
E N D
Angle-Side-Angle (ASA) Congruence Postulate E F 4cm B C 4cm D A
If two angles and the ______________ side of one triangle are _____________ to two angles and the ____________ side of a second triangle, then the two triangles are ________________. included congruent included congruent
Angle-Angle-Side (AAS) Congruence Theorem E F B C D A
OR Angle-Angle-Side (AAS) Congruence Theorem E F B C D A
nonincluded If two angles and a _____________________ side of one triangle are _______________ to two angles and the corresponding ____________________ side of a second triangle, then the two triangles are ________________. congruent nonincluded congruent
Does AAA work? NO!
Does ASS work? No! There is no ASS in geometry!
Given: Prove: ∆ABC ∆DCB Statements Reasons Given 1. 1. alternate interior angles 2. BCD CBA 2. 3. Given 3. alternate interior angles 4. BCA CBD 4. Reflexive Prop. 5. BC BC 5. ASA 6. ∆ABC ∆DCB 6.
Given: Prove: Statements Reasons Given 1. 1. Def. of segment bisector 2. 2. 3. Given 3. vertical angles 4. ABD EBC 4. AAS 5. ∆ABD ∆EBC 5.
Decide whether the triangles are congruent. Explain your reasoning. Yes, ASA
Decide whether the triangles are congruent. Explain your reasoning. Yes, AAS
Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS
Decide whether the triangles are congruent. Explain your reasoning. No, ASS doesn’t work!
Decide whether the triangles are congruent. Explain your reasoning. Yes, AAS