Isosceles Triangles

1
Isosceles Triangles

• Chapter 4 Day 13

2
Isosceles vs. Equilateral

• Recall that
• An isosceles triangle is a triangle in which at
  least two sides are congruent.
• An equilateral triangle is a triangle with all
  sides congruent.

• What do we know about equilateral triangles?

3
Properties of Equilateral Triangles

• The Isosceles Triangle Theorems also apply to
  equilateral triangles.
• This leads to 2 corollaries about the angles of
  an equilateral triangle.

4
Properties of Equilateral Triangles

• If a triangle is equilateral then it is
  equiangular.
• If a triangle is equilateral, then each angle
  measures 60 degrees.

5
Prove it!!!

• Lets prove the first corollary!
• If a triangle is equilateral then it is
  equiangular.Given Equilateral triangle
  ABC.Prove Triangle ABC is equiangular.

6
Proof
Statements Reasons

• 1. ?ABC is an equilateral triangle 1. Given
• 2. AB ?? AC ? BC 2. An equilateral ? is a
  ?
• with all 3 sides ?.
• 3. ?A ? ?B ? ?C 3. If two sides of a ?
  are ? then the angles opposite
  those sides are ?
• 4. ?ABC is an equiangular triangle 4. An
  equiangular ? is a ? with all angles ?.

7
Use Properties of Equilateral Triangles

• Draw line segment EJ so that EJ bisects ?2 and J
  lies on FG.
• Find m?HEJ and m?EJH
• 15, 75
• Find m?EJG
• 105

J