This document discusses properties of isosceles triangles. It states that an isosceles triangle has at least two sides of equal length. The base angles of an isosceles triangle are always congruent. If a triangle has two congruent angles, then it is an isosceles triangle. An equilateral triangle is a special type of isosceles triangle where all three sides are congruent and all three angles are congruent.

1. Properties of Isosceles Triangles Objectives: Discover a relationship between the base angles of an isosceles triangle.

2. Isosceles Triangle – at least two sides have the same length 9 9 4 3 miles 3 miles 8 miles 5 5 5

3. equilateral triangle : isosceles triangle with all three sides are congruent 7 7 7

4. Parts of Isosceles Triangle : vertex angle – between two  sides

5. Parts of Isosceles Triangle : base angles – angles opposite  sides

6. Parts of Isosceles Triangle : base – side opposite vertex

7. Name each part of the isosceles triangle below. vertex angle

8. Name each part of the isosceles triangle below. base

9. Name each part of the isosceles triangle below. base angles

10. Isosceles Triangle Theorem If a triangle is isosceles, then _______________________. base angles are congruent

11. Converse of Isosceles Triangle : If a triangle has two congruent angles, it is an isosceles triangle.

12. Equilateral Triangle: An equilateral triangle is equiangular and an equiangular triangle is equilateral.

13. Find the missing angle measures. 68 44 a m  a = m  b= b 68

14. Find the missing angle measures. 119 30.5 c m  c = m  d= d 30.5

15. Find the missing angle measures. 60 60 e m  e = m  f = m  g = f 60 g