Download The Isosceles Triangle Theorems

November 30, 2015
4.4
The Isosceles Triangle Theorems
November 30, 2015
AB ⊥ BD, AB||DE,
CF BISECTS AE AND BD
A
AB = DE
F
C
D
B
What can you
conclude?
E
November 30, 2015
4.4 Objectives
1) Apply the theorems and corollaries about isosceles
triangles
2) Use the AAS Theorem to prove two triangles
congruent
3) Use the HL Theorem to prove two right angles
congruent
4) Prove that two overlapping triangles are congruent
November 30, 2015
November 30, 2015
November 30, 2015
November 30, 2015
November 30, 2015
The Transamerica Pyramid
in San Francisco
Each of its four faces is an
isosceles triangle, with two
congruent sides.
The congruent sides are
called legs, and the third
side is called the base.
There are also two base
angles and one vertex
angle.
base
base angle
leg
vertex angle
base angle
leg
Label the isosceles triangle.
November 30, 2015
Theorem 4-1
The Isosceles Triangle Theorem
If two sides of a triangle are
congruent, then the angles
opposite to those sides are
congruent.
November 30, 2015
Three Corollaries based on Theorem 4-1
Corollary 1
An equilateral triangle is also equiangular.
Corollary 2
An equilateral triangle has three 60˚ angles
Corollary 3
The bisector of the vertex angle of an
isosceles triangle is perpendicular to the
base at its midpoint.
November 30, 2015
November 30, 2015
Theorem 4-2
If two angle of a triangle are
congruent, then the sides
opposite those angles are
congruent.
(Converse of Theorem 4-1)
November 30, 2015
One Corollary based on Theorem 4-2
Corollary
An equilateral triangle is also equilateral
November 30, 2015
November 30, 2015
November 30, 2015
November 30, 2015
November 30, 2015
Proof
November 30, 2015
November 30, 2015