9.7
Special Right Triangles
Objective:
After studying this section, you will be able to identify
the ratio of side lengths in a 30°-60°-90° triangle and
in a 45°-45°-90° triangle.
Theorem
In a triangle whose angles have the measures 30°,
60°, and 90°, the lengths of the sides opposite these
angles can be represented by a, a 3 , and 2a
respectively.
(30°-60°-90° Triangle Theorem)
60°
2a
a
30°
a 3
NOTE: This information can also be found on
your AIMS Reference Sheet!
And now…for the moment of Proof!
C
Given: Triangle ABC is equilateral
30°
CD bisects ACB
2a
Prove:
The ratio of AD:DC:AC = a : a 3 : 2a
60°
A
(Hint: use a paragraph proof!)
a
D
B
Theorem
In a triangle whose angles have the measures 45°,
45°, and 90°, the lengths of the sides opposite these
angles can be represented by a, a, and a 2
respectively.
(45°-45°-90° Triangle Theorem)
45°
a 2
a
45°
a
Example 1:
Example 2:
Find BC and AC
Find JK and HK
H
A
10
6
60°
B
C
K
60°
J
Last 2 practice problems…
Example 3:
Example 4:
MOPR is a square.
Find ST and TV
T
Find MP
M
R
V
9
O
P
45°
4
S
Summary…
State how to classify triangles. Explain in your own
words the Pythagorean Theorem.
Classwork…
Break up into groups of 3 or 4. All groups will be given
a special right triangle problem and a designated
whiteboard. Once the group has solved for the missing
sides, 1 representative will hold up the group’s
whiteboard. The group with the most points will be
dubbed Special Right Triangles Royalty!
Homework
Worksheet 9.7 Special Right Triangles
Parts 1 and 2!