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4.6 Isosceles Triangles What you’ll learn: 1.To use properties of isosceles triangles 2.To use properties of equilateral triangles.

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Parts of an isosceles Triangle Legs – the 2 congruent sides Base – the other side (it is not always sitting on the base) Vertex angle – angle formed by the 2 legs of the triangle. Base angle – angle formed by a leg and the base. leg Base Base angles Vertex Angle

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Theorems Theorem 4.9 – Isosceles Triangle Theorem If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. If AB BC, then A C. Theorem 4.10 If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent. If A C, then AB BC. A B CA B C

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Corollaries Corollary 4.3 A triangle is equilateral iff it is equiangular. Corollary 4.4 Each angle of an equilateral triangle measures 60 .

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Given: AB=CB=BD, ACB BCD Prove: A D 1.AB=CB=BD, ACB BCD 2. A ACB D BCD 3. A D 1.Given 2.Isosceles triangle theorem 3.Substitution C D B A

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Examples Use the figure. a.Name 2 congruent angles MLN N b.Name 2 congruent segments. PM PL Use the figure to find x a. 2x+6x+6+6x+6=180 14x+12=180 x=12 b. x+x+3x=180 x=36 P L M N (6x+6) 2x xx 3x

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Homework p. 219 10-30 even 35-37 all

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Quiz Tell whether the pair of triangles is congruent or not and why. 1. 2.

Quiz Tell whether the pair of triangles is congruent or not and why. 1. 2.

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