Download Properties of Isosceles Triangles

4.7 Use Isosceles and Equilateral Triangles
1.
2.
Objectives:
To complete and use the Base Angles Theorem and
its converse
To deduce the Equilateral Triangle Theorem from
the Base Angles Theorem
Definition: Review
A triangle is an isosceles triangle if and only if it has
at least two congruent sides.
Investigation
What relationship do you notice about the base angles
of each isosceles triangle?
Base Angles Theorem:
If two sides of a triangle are
congruent, then the angles
opposite them are
congruent.
Example
Given: AC  AB
Prove B  C
C
A
Median
M
B
Example
Given: AC  AB
Prove B  C
Example
Find the value of x.
2x+5
30
Example: SAT
If AB = BC, what is y in terms of x?
A
3x - 2
B
2y
C
Investigation
What about the
converse of the Base
Angles Theorem.
Converse of the Base Angles Theorem:
If two angles of a triangle
are congruent, then the
sides opposite them are
congruent.
Equilateral Triangle Theorem
A triangle is equilateral if and only if it is equiangular.

Example
Find the values of x and y in the diagram.
Example: SAT
Find the value of x.
x
18
60
24
60
Example: SAT
In the figure shown, if O is
the center of the circle,
what is the value of x?
O
70
x
Example: SAT
In the figure shown, if AB = AC and
AC||BD, what is the value of x?
130
B
A
C
x
D