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Chapter 3: Polygons and Their Relations

# Congruence of Triangles

When we compare two triangles, the most time we want to see if they are congruent or equal in size. The most obvious way that two triangles are congruent is that they have three congruent sides or angles. There are also many other ways to prove that two triangles are congruent. I have listed them below:

SAS Postulate for Congruence of Triangles: If two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of a second triangle, then the triangles are congruent.

SSS Postulate for Congruence of Triangles: If the three sides of one triangles are congruent to the corresponding three sides of a second triangle, then the triangles are congruent.

ASA Postulate for Congruence of Triangles: If two angles and the included side of one triangle are congruent to the corresponding two angles and included side of a second triangle, then the triangles are congruent.

Third Angle Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

AAS Theorem: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent.

Hypotenuse-Leg (HL) Theorem: Two right triangles are congruent if the hypotenuse and a leg of one are congruent, respectively, to the hypotenuse and corresponding leg of the other.

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