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# Congruent Triangles

### theorems and postulates relating to congruent triangles (chp. 4)

Hypothesisconclusion
The sum of the measures of the angles of a triangle 180
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent
The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
The acute angles of a right triangle are complementary
There can be at most one right or obtuse angle in a triangle
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent
If two angles and the included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent
If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent
Congruence of triangles is reflexive, symmetric, and transitive
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle the triangles are congruent
If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triagle, then the two triangles are congruent
If one leg and an acute angle of one right triangle are congruent to the corrsponding leg and acute angle of another right triangle, then the triangles are congruent
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
If two angles of a triangle are congruent, then the sides opposite those angles are congruent
A triangle is equilateral if and only if it is equiangular
Each angle of an equilateral triangle measures 60 degrees
Created by: m.meyer