Proving Triangles Congruent

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Presentation transcript:

Proving Triangles Congruent Sections 4.3-4.5

Side-side-side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence Theorem 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 two triangles are congruent.

Hypotenuse-Leg (HL) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

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 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.

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

Proving with SSS Prove triangle KLM is congruent to triangle NLM

Prove that triangle RST is congruent to triangle VUT

Assignment pg. 237 #1-4, 16-19 pg. 243 #3-8, 20-22