Transcript Properties of Isosceles Triangles

Warm-Up 1
If the lengths of two sides of an isosceles
triangle are 3 and 7, what is the perimeter
of the triangle?
Warm-Up 2
Use your
straightedge to
draw an acute
angle. How could
you use your
compass to turn
this angle into an
isosceles
triangle?
Definition: Review
A triangle is an isosceles triangle if and
only if it has at least two congruent sides.
4.7 Use Isosceles and Equilateral Triangles
Objectives:
1. To complete and use the Base Angles
Theorem and its converse
2. To deduce the Equilateral Triangle
Theorem from the Base Angles Theorem
Base Angles Theorem:
If two sides of a triangle
are congruent, then
the angles opposite
them are congruent.
Example 1
C
1.
2.
3.
4.
5.
AC = AB
Given
BM = CM
Def. of Median
AM = AM
Reflex A
AMC = AMB SSS
<B = <C
CPCTC
Median
M
B
Example 2
Try this one in your notebook
Example 3
Find the value of x.
2x+5
30
35
Example 4: SAT
If AB = BC, what is y in terms of x?
A
3x - 2
B
2y
y=2x-4
C
Converse of the Base Angles Theorem:
If two angles of a
triangle are
congruent, then the
sides opposite them
are congruent.
Investigation 3
In this Investigation,
we will use some
more compass and
straightedge
wizardry to
construct a perfect
equilateral triangle.
Investigation 3
1. Draw AB.
A
B
Investigation 3
2. Using A as center and AB as the radius,
draw a quarter-circle arc through B.
A
B
Investigation 3
3. Using B as center and AB as the radius,
draw a quarter-circle arc through A.
A
B
Investigation 3
4. Label the point of intersection C.
C
A
B
Investigation 3
5. Draw AC and BC.
C
A
B
Investigation 3
Click button
below to watch
a construction
video
Investigation 3
In ΔABC, measure each angle with the
protractor. What do you notice about the
angle measurements?
Use deductive reasoning to show that these
measurements must be true based on the
Base Angles Theorem.
Equilateral Triangle Theorem
A triangle is equilateral if and only if it is
equiangular.

Example 5
Find the values of x and y in the diagram.
Answer in
your
notebook
Example 6: SAT
Find the value of x.
x
18
60
30
24
60
Example 7: SAT
O
70
x
In the figure shown, if
O is the center of
the circle, what is
the value of x?
55
Example 8: SAT
In the figure shown, if
AB = AC and
AC||BD, what is the
value of x?
130
B
65
A
C
x
D