# 4.5 Proving Δs are  : ASA and AAS & HL

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4.5 Proving Δs are  : ASA and AAS & HL

Objectives: Use the ASA Postulate to prove triangles congruent
Use the AAS Theorem to prove triangles congruent

Postulate 4.3 (ASA): Angle-Side-Angle 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.

Theorem 4.5 (AAS): Angle-Angle-Side 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.

Example 1: Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

Example 1: In addition to the angles and segments that are marked, EGF JGH by the Vertical Angles Theorem. Two pairs of corresponding angles and one pair of corresponding sides are congruent. Thus, you can use the AAS Congruence Theorem to prove that ∆EFG  ∆JHG.

Example 2: Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

Example 2: In addition to the congruent segments that are marked, NP  NP. Two pairs of corresponding sides are congruent. This is not enough information to prove the triangles are congruent.

Example 3: AD ll CE Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. Answer: ASA Congruence Postulate

Hypotenuse- Leg (HL) Congruence Theorem:
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent. Example: because of HL. A X B C Y Z

Examples: Determine if the triangles are congruent
Examples: Determine if the triangles are congruent. State the postulate or theorem.

Triangles are congruent when you have…
SSS AAS SAS ASA HL

Triangles are not congruent when you have…
ASS or SSA AAA

Assignment Geometry: Worksheet

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