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Geometry

Geometry. 4.6: Isosceles and Equilateral 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 . Vertex Angle. Base Angle. Base Angle. Base Angles Theorem.

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Geometry

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  1. Geometry 4.6: Isosceles and Equilateral Triangles

  2. 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. Vertex Angle Base Angle Base Angle

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

  4. Converse to the Base Angles Theorem • If two angles of a triangle are congruent, then the sides opposite them are congruent.

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

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

  7. C A C B A B A B C Yes Yes No

  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

  9. Practice Problems • Find the measure of the missing angles and tell which theorems you used. B B C A 50° A C m C=50° (Base Angle Theorem) m B=80° (Triangle Sum Theorem) m A=60° m B=60° m C=60° (Corollary to the Base Angles Theorem)

  10. More Practice Problems Is there enough information to prove the triangles are congruent? S T U R V No Yes No W

  11. Factoring Review • Solve

  12. Homework • Page 287: 9-22 all, 29-32 all, 38-39

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