Download Isosceles Triangles

Isosceles Triangles
Sec: 4.6
Sol: G.5
Properties of Isosceles Triangles
An isosceles triangle is a triangle with two congruent
sides.
The congruent sides are called legs and the third side is
called the base.
3
Leg
1
Vertex
Base Angles
Base
Leg
2
Theorem 4.9 Isosceles Triangle
Theorem
If two sides of a triangle are congruent, then the
angles opposite those sides (base angles) are
congruent.
If AB  AC , then B  C.
A
B
C
D
Given:
AB  CB  BD
ACB  BCD
C
B
Prove: A  D
A
Statement
1. AB  CB  BD
ACB  BCD
2.
ABC  DBC
3.
A  ACB
D  DCB
4.
5.
A  D (A  C  D)
Reason
Find the measure of the missing angle
If
DE  CD, BC  AC , AND
MCDE  120
What is the measure of BAC
D
B
C
A
E
Theorem 4.10
If two angles of a triangle are congruent, then the sides opposite
those angles are congruent.
A
If B  C , then AB  AC.
B
C
Example: Find the value of x. Since two angles are congruent, the
A
sides opposite these angles must be
congruent.
3x - 7
x+15
3x – 7 = x + 15
2x = 22
50  C
B 50 
X = 11
Lesson 3-2: Isosceles Triangle
7
Example:
• Name Two Congruent Angles:
B
C
A
D
• Name Two Congruent Segments:
Properties of Equilateral Triangles
Corollaries:
4.3 A triangle is equilateral if and only if it is
equiangular.
C
A
B
4.4 Each angle of an equilateral triangle
measures 60°.
C
60°
60°
A
60°
B
Example: Triangle EFG is equilateral,
and segment EH bisects angle E
Find the measure of angle 1 and 2:
E
Solve for X:
F
H
G
Assignments:
Classwork: WB pg 51 1-6
Homework: Worksheet 4-6