Chapter Four:  
Congruent Triangles

Geometry   Notes

Chapter  4

Section  4.1
Section  4.2
Section  4.3
Section  4.4
Section  4.5
Section  4.6
Section  4.7

Geometry Contents

Take notes on the following topics.

Section 4-5  Isosceles and Equilateral  Triangles

Vocabulary

Leg of an isosceles triangle (p.211) The leg of an isosceles triangle are the two congruent sides.

Base angles of an isosceles triangle (211) The base angles of an isosceles triangle are the two angles formed by the base and one of the congruent sides.

Vertex angle of an isosceles triangle (p.211) The vertex angle of an isosceles triangle is the angle formed by the congruent sides of the triangle.

Base of an isosceles triangle (p.211) The side opposite the vertex angle is called the base.

Corollary (p. 212) A corollary is a statement that follows directly from a theorem.

 

Theorem 4-3  Isosceles Triangle Theorem

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

Corollary 1 to Theorem 4-3

If a triangle is equilateral, then it is equiangular.

Corollary 2 to Theorem 4-3

Each angle of an equilateral triangle measures 60.

Theorem 4-4 Converse of the Isosceles Triangle Theorem

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

Corollary to Theorem 4-4

If a triangle is equiangular, then it is equilateral.

Theorem 4-5

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of  the base.