# Proving Triangles Congruent

for Geometry

## Terms

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- theorem
- if two angles of one triangle are congruent to two angles of a second triangle, then the third angles are also congruent
- base angles converse
- if two angles of a triangle are congruent, then the sides opposite them are congruent
- ASA postulate
- if two angles and the included side of one triangle are congruent to two angles and the included side of the second, the triangles are congruent
- hypotenuse-leg theorem
- if a hypotenuse and leg of a right triangle are congruent to a hypotenuse and a leg of a second right triangle, then the triangles are congruent
- theorem
- the acute angles of a right triangle are complementary
- exterior angles theorem
- the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
- reflexive property
- every triangle is congruent to itself
- cpctc
- corresponding parts of congruent triangles are congruent
- base angles theorem
- if two sides of a triangle are congruent, then the angles opposite them are congruent
- symmetric property
- if triangle ABC is congruent to triangle PQR, then triangle PQR is congruent to triangle ABC
- corollary
- if a triangle is equiangular, it is also equilateral
- theorem
- the sum of the angles of a triangle is 180 degrees
- SSS postulate
- if three sides of one triangle are congruent to three sides of a second, the triangles are congruent
- transitive property
- if triangle ABC is congruent to triangle PQR and triangle PQR is congruent to triangle TUV, then triangle ABC is congruent to triangle TUV
- corollary
- if a triangle is equilateral, it is also equiangular
- theorem
- the measure of the exterior angle of a triangle is greater than the measures of either of the two remote interior angles
- SAS postulate
- if two sides and the included angle of one triangle are congruent to two sides and the included angle of the second, the triangles are congruent
- AAS theorem
- if two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of a second, then the triangles are congruent