9.7 Special Right Triangles

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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.

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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, , and 2a
respectively. (30-60-90 Triangle
Theorem)
60
2a
a
30
NOTE This information can also be found on
your AIMS Reference Sheet!
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And nowfor the moment of Proof!
C
Given Triangle ABC is equilateral
30
2a
Prove The ratio of ADDCAC (Hint use a
paragraph proof!)
60
A
B
D
a
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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 respectively. (45-45-90
Triangle Theorem)
45
a
45
a
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Example 2 Find JK and HK
Example 1 Find BC and AC
H
A
10
6
60
60
C
J
B
K
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Last 2 practice problems
Example 4 Find ST and TV
Example 3 MOPR is a square. Find MP
T
M
R
45
V
S
4
9
P
O
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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 groups
whiteboard. The group with the most points will
be dubbed Special Right Triangles Royalty!
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Homework Worksheet 9.7 Special Right Triangles
Parts 1 and 2!