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Understanding Congruency Postulates: ASA and AAS Theorems

This text discusses the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates of triangle congruency. According to the 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 triangles are congruent. The AAS theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent. Examples are provided for better understanding.

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Understanding Congruency Postulates: ASA and AAS Theorems

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Presentation Transcript

  1. 4-3: Congruency Postulates Continued

  2. What congruency postulates do we know so far?

  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. H Q R F P G

  4. ~ ~ ~ Given: HF = HJ, ‹F = ‹J, ‹FHG = ‹JHK. ~ Can you say that ∆FGH = ∆JKH? J F Yes, they are congruent by ASA. K G H

  5. Angle-Angle-Side (AAS) Theorem If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. H Q R F P G

  6. ~ Given: RE = CA, ‹D = ‹T, ‹R = ‹C ~ ~ ~ R E C A Prove: ∆RED = ∆CAT T D If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent. ~ ∆RED = ∆CAT by ASA.

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