1. Isosceles and Equilateral Triangles

2. 4.5 Isosceles and Equilateral Triangles
Isosceles Triangle:
Vertex Angle
Leg
Leg
Base Angles
Base
*The Base Angles are Congruent*

3. Isosceles Triangles Theorem 4-3 Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent B
<A = <C A C

4. Isosceles Triangles
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 B
Given: <A = <C
Conclude: AB = CB A C

5. Isosceles Triangles Theorem 4-5
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base B
Given: <ABD = <CBD
Conclude: AD = DC and
BD is ┴ to AC A C D

6. Equilateral Triangles
If a triangle is equilateral, then the triangle
is equiangular
If a triangle is equiangular, then the triangle
is equilateral

7. Using Algebra
Find the values of x and y: M ) ) y° N x°
63° O L

8. Proof of the Isosceles Triangle Theorem
Statements
Reasons 1. 2. 3. 4. 5.

9. Find the values of the variables.

10. Find the values of the variables.