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Isosceles and Equilateral Triangles: Theorems, Properties, and Examples (100 characters)

Learn about isosceles and equilateral triangles, prove theorems, apply properties, and solve angle and value problems. (500 characters)

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Isosceles and Equilateral Triangles: Theorems, Properties, and Examples (100 characters)

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  1. Warm Up 1. Find each angle measure. True or False. If false explain. 2. Every equilateral triangle is isosceles. 3. Every isosceles triangle is equilateral.

  2. Objectives Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles.

  3. Recall that an isosceles triangle has at least two congruent sides. 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.

  4. Reading Math The Isosceles Triangle Theorem is sometimes stated as “Base angles of an isosceles triangle are congruent.”

  5. Example 2A: Finding the Measure of an Angle Find mF.

  6. Example 2B: Finding the Measure of an Angle Find mG.

  7. Check It Out! Example 2A Find mH.

  8. Check It Out! Example 2B Find mN.

  9. The following corollary and its converse show the connection between equilateral triangles and equiangular triangles.

  10. Example 3A: Using Properties of Equilateral Triangles Find the value of x.

  11. Example 3B: Using Properties of Equilateral Triangles Find the value of y.

  12. Check It Out! Example 3 Find the value of JL.

  13. Lesson Quiz: Part I Find each angle measure. 1. mR 2. mP Find each value. 3.x 4.y 5.x 6

  14. Lesson Quiz: Part II 6. The vertex angle of an isosceles triangle measures (a + 15)°, and one of the base angles measures 7a°. Find a and each angle measure.

  15. Assignment • Pg. 288 (3-10, 13-20, 22-26)

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