Download Properties of Isosceles Triangles

4.6 Isosceles Triangles
Objectives
Use properties of isosceles triangles
Use properties of equilateral triangles
Properties of Isosceles Triangles
The  formed by the ≅ sides is
called the vertex angle.
The two ≅ sides are called legs.
The third side is called the base.
vertex
leg
leg
The two s formed by the base
and the legs are called the
base angles.
base
Isosceles Triangle Theorem
Theorem 4.9
If two sides of a ∆ are ≅, then the s opposite
those sides are ≅ (if AC ≅ AB, then B ≅ C).
A
B
C
The Converse of Isosceles
Triangle Theorem
Theorem 4.10
If two s of a ∆ are ≅, then the sides
opposite those s are ≅ (if B ≅ C, then
AC ≅ AB).
Example 2:
Name two congruent angles (not indicated).
Answer:
Example 2:
Name two congruent segments (not indicated).
By the converse of the Isosceles Triangle Theorem, the
sides opposite congruent angles are congruent. So,
Answer:
Your Turn:
a. Name two congruent angles.
Answer:
b. Name two congruent
segments.
Answer:
Properties of Equilateral ∆s
Corollary 4.3
A ∆ is equilateral if it is equiangular.
Corollary 4.4
Each  of an equilateral ∆ measures 60°.
Example 3a:
EFG is equilateral, and
Find
and
bisects
bisects
Each angle of an equilateral triangle measures 60°.
Since the angle was bisected,
Example 3a:
is an exterior angle of EGJ.
Exterior Angle Theorem
Substitution
Add.
Answer:
Example 3b:
EFG is equilateral, and
Find
bisects
bisects
Linear pairs are supplementary.
Substitution
Subtract 75 from each side.
Answer: 105
Your Turn:
ABC is an equilateral triangle.
a. Find x.
Answer: 30
b.
Answer: 90
bisects
Assignment
Geometry:
Pg. 219 #9 – 28, 36, 40
Pre-AP Geometry:
Pg. 219 #9 – 30, 35 – 37, & 40