1. 4.6 Isosceles Triangles What you’ll learn: 1.To use properties of isosceles triangles 2.To use properties of equilateral triangles.

2. Parts of an isosceles Triangle Legs – the 2 congruent sides Base – the other side (it is not always sitting on the base) Vertex angle – angle formed by the 2 legs of the triangle. Base angle – angle formed by a leg and the base. leg Base Base angles Vertex Angle

3. Theorems Theorem 4.9 – Isosceles Triangle Theorem If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. If AB  BC, then  A  C. Theorem 4.10 If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent. If  A  C, then AB  BC. A B CA B C

4. Corollaries Corollary 4.3 A triangle is equilateral iff it is equiangular. Corollary 4.4 Each angle of an equilateral triangle measures 60 .

5. Given: AB=CB=BD,  ACB  BCD Prove:  A  D 1.AB=CB=BD,  ACB  BCD 2.  A  ACB  D  BCD 3.  A  D 1.Given 2.Isosceles triangle theorem 3.Substitution C D B A

6. Examples Use the figure. a.Name 2 congruent angles  MLN  N b.Name 2 congruent segments. PM  PL Use the figure to find x a. 2x+6x+6+6x+6=180 14x+12=180 x=12 b. x+x+3x=180 x=36 P L M N (6x+6)  2x  xx 3x 

7. Homework p. 219 10-30 even 35-37 all