Proving Triangles are Congruent

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Proving Triangles Congruent

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Presentation transcript:

Proving Triangles are Congruent Section 4.2 & 4.3

Side-Side-Side (SSS) Congruence Postulate If 3 sides of a triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent.

Are the following congruent?

Side-Angle-Side (SAS) Congruence Postulate If 2 sides and the included angle of one triangle are congruent to the 2 sides and the included angle of a second triangle, then the 2 triangles are congruent.

Are the following congruent?

Angle-Side-Angle (ASA) Congruence Postulate If 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.

Angle-Angle-Side (AAS) Congruence Postulate If 2 angles and a nonincluded side of 1 triangle are congruent to 2 angles and the nonincluded side of another triangle, then the 2 triangles are congruent.

Are the following congruent?

Are the following congruent?

Hypotenuse Leg (HL) If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.

One type that doesn’t work. AAA

Counterexample of AAA

The second type that doesn’t work. ASS

Counterexample of ASS

Are the following congruent?

Are the following congruent?

Are the following congruent?

Are the following congruent?