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Isosceles and Equilateral Triangles

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4.5 Isosceles and Equilateral Triangles

Isosceles Triangle: Vertex Angle Leg Leg Base Angles Base *The Base Angles are Congruent*

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Isosceles Triangles Theorem 4-3 Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent B <A = <C A C

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Isosceles Triangles Theorem 4-4 Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent B Given: <A = <C Conclude: AB = CB A C

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Isosceles Triangles Theorem 4-5

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base B Given: <ABD = <CBD Conclude: AD = DC and BD is ┴ to AC A C D

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Equilateral Triangles

If a triangle is equilateral, then the triangle is equiangular If a triangle is equiangular, then the triangle is equilateral

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Using Algebra Find the values of x and y: M ) ) y° N x° 63° O L

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Proof of the Isosceles Triangle Theorem

Statements Reasons 1. 2. 3. 4. 5.

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Find the values of the variables.

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Find the values of the variables.

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