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4.5 – Prove Triangles Congruent by ASA and AAS

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.

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4.5 – Prove Triangles Congruent by ASA and AAS

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  1. 4.5 – Prove Triangles Congruent by ASA and AAS

  2. Angle-Side-Angle (ASA) Congruence Postulate E F 4cm B C 4cm D A

  3. 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

  4. Angle-Angle-Side (AAS) Congruence Theorem E F B C D A

  5. OR Angle-Angle-Side (AAS) Congruence Theorem E F B C D A

  6. 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

  7. Does AAA work?

  8. Does AAA work? NO!

  9. Does ASS work? No! There is no ASS in geometry!

  10. 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.

  11. 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.

  12. Decide whether the triangles are congruent. Explain your reasoning. Yes, ASA

  13. Decide whether the triangles are congruent. Explain your reasoning. Yes, AAS

  14. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS

  15. Decide whether the triangles are congruent. Explain your reasoning. No, ASS doesn’t work!

  16. Decide whether the triangles are congruent. Explain your reasoning. Yes, AAS

  17. HW Problem

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