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4.6: Isosceles and Equilateral Triangles

Geometry 4.6: Isosceles and Equilateral Triangles

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The angle opposite the base is called the vertex angle.

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

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

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Converse to the Base Angles Theorem

If two angles of a triangle are congruent, then the sides opposite them are congruent.

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Corollary to the Base Angles Theorem

If a triangle is equilateral, then it is equiangular.

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Corollary to the Converse of the Base Angles Theorem

If a triangle is equiangular, then it is equilateral.

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C A C B A B A B C Yes Yes No

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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

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Practice Problems Find the measure of the missing angles and tell which theorems you used. B B A C 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)

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More Practice Problems

Is there enough information to prove the triangles are congruent? S T U R V No Yes No W

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Factoring Review Solve 𝑥 2 +𝑥−12

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Homework Page 287: 9-22 all, all, 38-39

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