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Isosceles and equilateral triangles

Isosceles and equilateral triangles. Section 4-5. Vocabulary . The congruent sides of an isosceles triangle are its legs . The third side is the base . The two congruent legs form the vertex angle . The other two angles are the base angles. Isosceles Triangle Theorem.

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Isosceles and equilateral triangles

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  1. Isosceles and equilateral triangles Section 4-5

  2. Vocabulary • The congruent sides of an isosceles triangle are its legs. • The third side is the base. • The two congruent legs form the vertex angle. • The other two angles are the base angles.

  3. Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite those sides are congruent. • If then

  4. Converse of the Isosceles Triangle Theorem • If two angles of a triangle are congruent, then the sides opposite those angles are congruent. • If then

  5. Theorem 4-5 • If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base.

  6. More theorems… • Corollary to Theorem 4-3 • If a triangle is equilateral, then the triangle is equiangular. • Corollary to Theorem 4-4 • If a triangle is equiangular, then the triangle is equilateral.

  7. Example 1 • Complete each statement. • 1. DBC  ?CDB • 2. BED  ?___ • 3. FED __?___ DFE • 4. AB _____  _______

  8. Example 2 • Solve for x and y. • A. x = 180-115 x = 65 y = 180-65-65 y = 50 • B. x + 5 = 60 x = 55 y – 10 = 60 y = 70

  9. assignment • Pg 254 #6-12, 16-19 show work

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