1. Holt Geometry 4-8 Isosceles and Equilateral Triangles 4-8 Isosceles and Equilateral Triangles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Geometry 4-8 Isosceles and Equilateral Triangles Do Now 1. Find each angle measure. True or False. If false explain. 2. Every equilateral triangle is isosceles. 3. Every isosceles triangle is equilateral.

3. Holt Geometry 4-8 Isosceles and Equilateral Triangles Apply properties of isosceles and equilateral triangles. Objective

4. Holt Geometry 4-8 Isosceles and Equilateral Triangles legs of an isosceles triangle vertex angle base base angles Vocabulary

5. Holt Geometry 4-8 Isosceles and Equilateral Triangles In an Isosceles triangle, the congruent sides are called the legs. The vertex angle is the angle formed by the legs. The side opposite the vertex angle is called the base, and the base angles are the two angles that have the base as a side. 3 is the vertex angle. 1 and 2 are the base angles.

6. Holt Geometry 4-8 Isosceles and Equilateral Triangles

7. Holt Geometry 4-8 Isosceles and Equilateral Triangles The Isosceles Triangle Theorem is sometimes stated as “Base angles of an isosceles triangle are congruent.” Reading Math

8. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 1: Astronomy Application The length of YX is 20 feet. Explain why the length of YZ is the same.

9. Holt Geometry 4-8 Isosceles and Equilateral Triangles Find mF. Example 2: Finding the Measure of an Angle

10. Holt Geometry 4-8 Isosceles and Equilateral Triangles Find mG. Example 3: Finding the Measure of an Angle

11. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 4 Find mH.

12. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 5 Find mN.

13. Holt Geometry 4-8 Isosceles and Equilateral Triangles The following corollary and its converse show the connection between equilateral triangles and equiangular triangles.

14. Holt Geometry 4-8 Isosceles and Equilateral Triangles

15. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 6: Using Properties of Equilateral Triangles Find the value of x.

16. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 7: Using Properties of Equilateral Triangles Find the value of y.

17. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 8 Find the value of JL.

18. Holt Geometry 4-8 Isosceles and Equilateral Triangles Lesson Quiz: Part I Find each angle measure. 1. mR 2. mP Find each value. 3. x 4. y 5. x 124° 28° 20 6 26°