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Congruent Triangles
theorems and postulates relating to congruent triangles (chp. 4)
| Hypothesis | conclusion |
|---|---|
| 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
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