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Mastering Isosceles and Equilateral Triangles Theorems

Understand properties and theorems of isosceles and equilateral triangles. Learn how congruent sides and angles relate, and solve examples to test your knowledge. Complete assigned problems to reinforce learning.

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Mastering Isosceles and Equilateral Triangles Theorems

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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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