1. Applied Geometry Lesson: 6 – 4 Isosceles Triangles Objective: Learn to identify and use properties of isosceles triangles.

2. Parts of an Isosceles Triangle

3. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite the sides are congruent.

4. Theorem 6-3 The median from the vertex angle of an isosceles triangle lies on the perpendicular bisector of the base and the angle bisector of the vertex angle.

5. x = 49 y = 90 Because is also a perpendicular bisector.

6. x = 65 y = 50 x = 90 y = 70

7. Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

8. 4x = 6x - 5 -2x = -5 x = 2.5 AC = 4(2.5) = 10 BC = 6(2.5) -5 = 10

9. Theorem 6-5 A triangle is equilateral if and only if it is equiangular.

10. Homework Pg. 249 1 – 5 all, 6 – 22 E