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ASA and AAS Congruence

ASA and AAS Congruence. Section 4.5. 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 two triangles are congruent. Angle-Angle-Side (AAS) Congruence Theorem.

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ASA and AAS Congruence

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  1. ASA and AAS Congruence Section 4.5

  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 two 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 two triangles are congruent.

  4. In the diagram at the right, what postulate or theorem can you use to prove that ? Explain. RSTVUT STATEMENTS REASONS Given S U Given RS UV The vertical angles are congruent RTSUTV GUIDED PRACTICE SOLUTION

  5. RTSUTV GUIDED PRACTICE ANSWER Therefore are congruent because vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem.

  6. Quick reference on pg. 252 • These are the only 5 ways to prove triangles are congruent • There is no SSA or AAA.

  7. Assignment • p. 252: 3-10, 14-17

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