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Proving Triangles are Congruent: ASA and AAS

Proving Triangles are Congruent: ASA and AAS. Geometry. Angle-Side-Angle (ASA) Congruence Postulate. If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

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Proving Triangles are Congruent: ASA and AAS

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  1. Proving Triangles are Congruent: ASA and AAS Geometry

  2. Angle-Side-Angle (ASA) Congruence Postulate • If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

  3. Angle-Angle-Side (AAS) Congruence Theorem • If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the triangles are congruent.

  4. Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

  5. Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

  6. U Z W X Ex. 1 Developing Proof UZ ║WX AND UW ║WX. Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. 1 2 3 4

  7. Ex. 2 Proving Triangles are Congruent Given: AD ║EC, BD  BC Prove: ∆ABD  ∆EBC Plan for proof: Notice that ABD and EBC are congruent. You are given that BD  BC Use the fact that AD ║EC to identify a pair of congruent angles.

  8. Proof: Statements: • BD  BC • AD ║ EC • D  C • ABD  EBC • ∆ABD  ∆EBC Reasons: • Given • Given • Alternate Interior Angles • Vertical Angles Theorem • ASA Congruence Theorem

  9. Note: • You can often use more than one method to prove a statement. In Example 2, you can use the parallel segments to show that D  C and A  E. Then you can use the AAS Congruence Theorem to prove that the triangles are congruent.

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