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```					   Solve for x in the following 45-45-
90 triangles

10             X                  x
10 3

What is the rule with the 45-45-90 triangle?
30- 60 -90 Triangle
A 30-60-90 is an
equilateral triangle
that is bisected!! 

Section 5.9
Triangle ABC is equilateral, and
CD is an altitude or height.

1. What are m A and m  B? _________
2 cm             2 cm      2. What are m ACD and m BCD? _______

3. What are m  ADC and m BDC? _______

4. What is the length of AD? ___________
CD bisects ACB             5. How do AC and AD compare?
________________________________

6. Use the Pythagorean Theorem to find the length of the other leg.
Simplify the square root.
A 30-60-90 Triangle is also known as
a bisected equilateral triangle.

60

a              2a
30

a 3
Triangle ABC is equilateral with side
lengths of 3 in. Find the height, CD .
Step 1: Label the degrees
of the triangles.
Step 2: Label the sides of
the triangles.
What is the length of AD ?
Step 3: What is the length
of CD ?
Examples: Find the missing
sides.

1.                  2.
Examples: Find the missing
sides.

3.                  4.
7
60
4 2

30
9

What happens when
60
you are given the
longest leg?

Find the missing sides in the triangles
below.
b.         c.
a.

9 2

30                        30

12                          5
60
Extra Practice Problems
30
30

60
32               60

5

30
30

10
2 20
60
60
Examples Continued:
a.   Find the altitude of an Equilateral
triangle with perimeter 18 feet.

b.   Find the side of an equilateral triangle
with altitude 6 cm.

SKHmath
Application:
An ornamental pin is in the shape of an
equilateral triangle. The length of each
side is 6 centimeters. Josh will attach
the fastener to the back along AB. Will
the fastener fit if it is 4 centimeters
long?

```
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