1. Section 4.5 isosceles & equilateral triangles
Geometry

2. Isosceles Triangle
Legs are congruent
Vertex Angle
Legs
Base Angles

3. Theorem 4-3 (Isosceles Triangle Thm): If two sides of a triangle are congruent, then the angles opposite those sides are congruent. c b a

5. Theorem 4-4 (Converse of Isosceles Triangle Thm): If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

6. Theorem 4-5
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. A B C

7. Ex. 2)
Find the values of x and y. M y° x°
63° L N

8. Corollary: a statement that follows immediately from a theorem
Corollary to Thm 4-3: If a triangle is equilateral, then it is equiangular.
Corollary to Thm 4-4: If a triangle is equiangular, then it is equilateral.

9. Ex. 3) If
find A B C M

10. Ex. 4) A If
find B C M

11. Ex. 5) A
If and
find x. B C M

12. Ex. 6) Find the missing angles and sides.