Geometry Chapter 4 Theorems and Definitions

Theorems for chapter 4

Isosceles Triangles

2 sides and 2 angles are congruent

Isosceles Triangle Theorem

If 2 sides of a triangle are congruent, then angles opposite those sides are congruent.

Converse of the Isosceles Triangle Theorem

If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent.

Theorem

If a line bisects the vertex angle of an isosceles triangle, then the line is the perpendicular bisector of the base.

Equilateral Triangles

All sides are congruent

Corollary

A theorem that can be proved easily using another theorem

Corollary to Isosceles Triangle Theorem

If a triangle is equilateral, then it is equiangular.

Corollary to converse of the Isosceles Triangle Theorem

If a triangle is equiangular, then it is equilateral.

Right Triangle

Has one 90 degree angle

Hypotenuse-Leg Theorem (H-L)

If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and a leg of another triangle, then the triangles are congruent.