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Chapter 4.6

Chapter 4.6. Isosceles, Equilateral, and Right Triangles. Objectives/Assignment. Use properties of isosceles and equilateral triangles Use properties of right triangles Assignment: 1-25 all. Goal 1: Using Properties of Isosceles Triangles.

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Chapter 4.6

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  1. Chapter 4.6 Isosceles, Equilateral, and Right Triangles

  2. Objectives/Assignment • Use properties of isosceles and equilateral triangles • Use properties of right triangles • Assignment: 1-25 all

  3. Goal 1: Using Properties of Isosceles Triangles • The two angles in an isosceles triangle adjacent to the base of the triangle are called base angles. • The angle opposite the base is called the vertex angle.

  4. Theorem 4.6: Base Angles Theorem • If two sides of a triangle are congruent, then the angles opposite them are congruent. A C B

  5. Theorem 4.7: Converse to the Base Angles Theorem • If two angles of a triangle are congruent, then the sides opposite them are congruent. A C B

  6. Corollary to the Base Angles Theorem 4.6 • If a triangle is equilateral, then it is equiangular.

  7. Corollary to the Converse of the Base Angles Theorem 4.7 • If a triangle is equiangular, then it is equilateral.

  8. Examples C A C B A B A B C NO YES YES

  9. Goal 2: Using Properties of Right Triangles Theorem 4.8 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. A D B F C E

  10. Practice Problems • Find the measure of the missing angles and tell which theorems you used. B B C A 50° A C

  11. More Practice Problems Is there enough information to prove the triangles are congruent? S T U R V W

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