Geometry Section 4.6

Isosceles Triangle Theorem

Goals for today:

1. Identify the parts of an isosceles triangle.

2. Learn and apply the Isosceles Triangle Theorem and its converse.

Recall that an isosceles is a triangle with _________________.

The congruent sides are called the ____ and the noncongruent side is calledthe_____. The angle formed by the two legs is called the ___________ while the two angles at each end of the base are called ___________.

two congruent sides

legs

basevertex angle

base angles

Theorem 4.6 Isosceles Triangle Theorem (ITT)If two sides of a triangle are congruent, then the angles

opposite those sides are congruent.

CA

Theorem 4.7 Converse of the Isosceles Triangle Theorem (ITTC)

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

those angles are congruent.

Examples: Solve for x.

5.31

632

1801172

1806464112

x

x

x

x

10971180

712/142

14238180

603/180 5.11

223

128116

x

x

xx

5.10

221

15563

x

x

xx

Classify ABC according to its angles and sides.

A

B C450

5.672/13545180

isosceles acute