Question

Prove the Isosceles Base Angles Theorem

Given: GB GD, GU bisects ZDGB
Prove: ZB ZD
Statements
1. GB = GD
2.
3.
4. GU GU
5.
6. ZB ZD
Reasons
1. Given
2.
3. Definition of bisects
4.
5.
6.

Answer 1

The Isosceles Base Angles Theorem states that if two sides of a triangle are equal, then the angles opposite to those sides are equal.

Given: GB = GD

Since GB = GD, triangle ZDGB is isosceles.

By definition of bisects, GU bisects ZDGB.

By the Angle Bisector Theorem, ZG/ZU = GD/GU.

Because GB = GD, ZG = ZU.

By substitution, ZG/ZU = ZG/ZU. Hence, ZB = ZD.

Therefore, ZB ZD, which proves the Isosceles Base Angles Theorem.