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4.6 Isosceles, Equilateral, and Right Triangles

4.6 Isosceles, Equilateral, and Right Triangles . Standard 5.0 Goal: Use properties of isosceles, equilateral, and right triangles. Goal 1: Using Properties Of Isosceles Triangles.

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4.6 Isosceles, Equilateral, and Right Triangles

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  1. 4.6 Isosceles, Equilateral, and Right Triangles Standard 5.0 Goal: Use properties of isosceles, equilateral, and right triangles

  2. Goal 1: Using Properties Of Isosceles Triangles • In Lesson 4.1, you learned that a triangle is isosceles if it has at least two congruent sides, then they are the legs of the triangle and the non congruent side is the base. The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle.

  3. Theorems • Theorem 4.6 Base Angles Theorem: If two sides of a triangle are congruent, then the angles opposite them are congruent. • If AB = AC, Then <B = <C

  4. Theorem 4.7 • Converse Of the Base Angle Theorem: • If two angles of a triangle are congruent, then the sides opposite them are congruent. • If <B =<C, then AB =AC

  5. Example #1 proof of the Base Angles Theorem • Given: ∆ABC, AB =AC • Prove: <B=<C

  6. Corollaries • Corollary To theorem 4.6 • If a triangle is equilateral, then it is equiangular. • Corollary To Theorem 4.7 • If a triangle is equiangular, then it is equilateral.

  7. Example #2 • Using Equilateral and Isosceles Triangles • 3x=180 • X=60

  8. Theorem Theorem 4.6 Hypotenuse-Leg (HL) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

  9. Example # 3 Proving Right Triangles Congruent • Given: AE  EB, AE  EC • AE  ED, AB =AC =AD • Prove: AEB = ABC = AED • Solution • Paragraph Proof You are given that

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