4-5 isosceles and equilateral triangles. the congruent sides of an isosceles triangle are its legs...

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4-5 Isosceles and Equilateral Triangles

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Page 1: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

4-5 Isosceles and

Equilateral Triangles

Page 2: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

• 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

Page 3: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Isosceles Triangle Theorem

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

Page 4: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Converse of the Isosceles Triangle Theorem

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

Page 5: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Problem 1: Using the Isosceles Triangle Theorems

Page 6: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form
Page 7: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

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

Page 8: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Problem 2: Using Algebra

What is the value of x?

Page 9: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Corollary: is a theorem that can be proved easily using another theorem.

A corollary is a theorem, so you can use it as a reason in a proof.

Page 10: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Corollary to Theorem 4-3

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

Page 11: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Corollary to Theorem 4-4

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

Page 12: 4-5 Isosceles and Equilateral Triangles. The congruent sides of an isosceles triangle are its legs The third side is the base The two congruent legs form

Problem 3: Finding Angle MeasuresWhat are the measures of <A, <B, and <ADC in the photo?