1. Isosceles and Equilateral Triangles
Lesson 4-5

2. Isosceles Triangles
Legs – the congruent sides of an isosceles triangle
Base – the third side of an isosceles triangle
Vertex angle – formed by the congruent sides
Base angles – the angles adjacent to the base
Vertex angle
legs
base
base angles

3. Thm 4-3 Isosceles Triangle Thm.Q U E
Two sides of a triangle are congruent if and only if angles opposite those sides are congruent.
Then ÐE

4. Thm 4-5 U Q E M QE ^ UM UM bisects QE
The bisector of the vertex angle of an isosceles triangles is the perpendicular bisector of the base. M
QE ^ UM
UM bisects QE

5. Using the Isosceles Triangle Thm.
Explain why DABC is isosceles.

6. Using Algebra with the Isosceles Triangle Thm
Suppose that mL = y. Find the values of x and y.
x = 90 and y = 45.

7. An angle exterior to the vertex of an isosceles triangle measures 80
An angle exterior to the vertex of an isosceles triangle measures 80. Find the angle measures of the triangle.
80° 1 3 2

8. Equilateral Triangles
If you have an Equilateral Triangle, then all the angles are congruent.
If you have an Equiangular Triangle, then all the sides are congruent.