# 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

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