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Transcript
Geometry Name: ______________________ (4-4 & 4-5) Triangles Congruence Theorems Date: ______________________ Objective: You will be able to determine if two triangles are congruent using the triangle congruency theorems. Triangle Congruency Theorems Side-Side-Side Congruence Postulate (SSS): If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Side-Angle-Side Congruence Postulate (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. 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 triangles are congruent. Angle-Angle-Side Congruence Postulate (AAS): If two angles and a non-included side of one triangle are congruent to two angles and the non-included side of a second triangle, then the triangles are congruent. Hypotenuse-Leg (HL): RIGHT TRIANGLES ONLY!! If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of a second right triangle, then the right triangles are congruent. Example #1: Are the following triangles congruent? If so, write a congruency statement and state by which triangle congruency theorem. 1. 2. 3. 4. 5. Example #2: What other information do you need in order to prove these triangles congruent? Example #3: Name the two congruent triangles in this picture.