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4-8 Triangles 4-8 Isosceles Isoscelesand and Equilateral Equilateral Triangles Warm Up Lesson Presentation Lesson Quiz Holt Geometry 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. Holt Geometry 4-8 Isosceles and Equilateral Triangles Objective Apply properties of isosceles and equilateral triangles. Holt Geometry 4-8 Isosceles and Equilateral Triangles Vocabulary legs of an isosceles triangle vertex angle base base angles 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. Holt Geometry 4-8 Isosceles and Equilateral Triangles Holt Geometry 4-8 Isosceles and Equilateral Triangles Reading Math The Isosceles Triangle Theorem is sometimes stated as “Base angles of an isosceles triangle are congruent.” 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. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 2: Finding the Measure of an Angle Find mF. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 3: Finding the Measure of an Angle Find mG. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 4 Find mH. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 5 Find mN. Holt Geometry 4-8 Isosceles and Equilateral Triangles The following corollary and its converse show the connection between equilateral triangles and equiangular triangles. Holt Geometry 4-8 Isosceles and Equilateral Triangles Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 6: Using Properties of Equilateral Triangles Find the value of x. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 7: Using Properties of Equilateral Triangles Find the value of y. Holt Geometry 4-8 Isosceles and Equilateral Triangles Example 8 Find the value of JL. Holt Geometry 4-8 Isosceles and Equilateral Triangles Lesson Quiz: Part I Find each angle measure. 1. mR 28° 2. mP 124° Find each value. 3. x 5. x Holt Geometry 20 4. y 26° 6
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