1. 4.5: Isosceles and Equilateral Triangles Objective: To use and apply properties of isosceles and equilateral triangles.

2. Isosceles Triangles 2 congruent legs Third side is the base The 2 congruent sides form the vertex angle The other 2 angles are the base angles. Vertex Angle Base Angles Legs BASE

3. Isosceles Triangle Theorem If a triangle is isosceles, then the base angles are congruent. C A B

4. Converse of Isosceles Triangle Theorem If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. (Therefore, it’s an isosceles triangle) C A B

5. THEOREM: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. C AB bisects D

6. Find the value of the variables. 54⁰ x y

7. Find the values of the variables. 1.2. y° 63° x° 4 cm z x° 65°

8. How do we know that triangle RST is isosceles? R U T W S V

9. How do you know is isosceles? A CB

10. Corollary: A statement that immediately follows a theorem. Corollary to the Isosceles Triangle Theorem: If a triangle is equilateral, then it is equiangular Corollary to converse of Isosceles Triangle Theorem : If a triangle is equiangular, then it is equilateral. A B C B A C

11. Find the values of the variables. 1.2. 4x 60 The perimeter is 54 cm. NOT DRAWN TO SCALE!! y° 60° x°

12. Find the value of the variables. The perimeter is 45 ft. (4y) (2x +1)