Congruence and Inequality Properties in an Isosceles Triangle

Congruence and Inequality Properties in an Isosceles Triangle

The Isosceles Triangle Theorem
-If two sides of a triangle are congruent, then the angles opposite these sides are congruent

Corollary
-each equilateral triangle is equiangular
-each angle of an equilateral triangle has a measure of 60 degrees.

Converse of Isosceles Triangle Theorem
-If two angles of a triangle are congruent, then the sides opposite these angles are congruent.
Corollary
-every equiangular triangle is equilateral.

Side Angle Inequality Theorem
-If one side of a triangle is longer than the second side, then the measure of the angle opposite the longer side is greater than that of the measure of the angle opposite the shorter side.

Angle Side Inequality Theorem
-If one side of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite to the smaller angle.

The Hinge Theorem
-If two sides of one triangle are congruent to two sides of a second triangle and the included angle of the first triangle has a greater measure than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

The Converse of The Hinge Theorem
-If two sides of one triangle are congruent to two sides of a second triangle, and the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is longer than the included angle of the second triangle.