5.3 Proving Triangles are congruent:

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Presentation transcript:

5.3 Proving Triangles are congruent: ASA and AAS

Angle-Side-Angle Congruence Postulate (ASA) 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.

Example 1 (a) Based on the diagram, can you use the ASA Congruence Postulate to show that the triangles are congruent? Explain your reasoning.

Example 1 (b) Based on the diagram, can you use the ASA Congruence Postulate to show that the triangles are congruent? Explain your reasoning.

Angle-Angle-Side Congruence Theorem (AAS) 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.

Example 2

Example 3 (a) Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use.

Example 3 (b) Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use.

Example 3 (c) Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use.

Example 4

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