Chapter%207%20Lesson%203

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Chapter 7 Lesson 3

• Objective To use the properties of
  45-45-90 triangles.

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Theorem 7-8 45-45-90 Triangle Theorem In a
45-45-90 triangle, both legs are congruent and
the length of the hypotenuse is v2 times the
length of a leg. Hypotenuse v2leg
45
hypotenuse
leg
45
leg
45
xv2
x
45
x
3
Example 1Finding the Length of the Hypotenuse
Find the value of each variable.
a.
b.
9
2v2
x
h
hv29 h9v2
xv22v2 x4
4
Example 2Finding the Length of the Hypotenuse
Find the length of the hypotenuse of a
45-45-90 triangle with legs of length 5v3.
5v3
5v3
xv25v3 x5v6
x
5
Example 3Finding the Length of the Hypotenuse
Find the length of the hypotenuse of a
45-45-90 triangle with legs of length 5v6.
5v6
5v6
xv25v6 x5v12 x5v(43) x10v3
x
6
Example 4Finding the Length of a Leg
Find the value of x.
6v2x
6
x
7
Example 5Finding the Length of a Leg
Find the length of a leg of a 45-45-90
triangle with a hypotenuse of length 10.
10v2x
10
x
8
Example 6Finding the Length of a Leg
Find the length of a leg of a 45-45-90
triangle with a hypotenuse of length 22.
22v2x
22
x
9
Theorem 7-9 30-60-90 Triangle Theorem In a
30-60-90 triangle, the length of the
hypotenuse is twice the length of the shorter
leg. The length of the longer leg is v3 times the
length of the shorter leg. hypotenuse 2
shorter leg longer leg v3 shorter leg
hypotenuse
long leg
2x
xv3
short leg
x
10
Example 7Finding the Lengths of the Legs
Find the value of each variable.
Shorter Leg hypotenuse 2 shorter leg 8 2x x
4
Longer Leg longer leg v3 shorter leg y
xv3 y 4v3
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Example 8Finding the Lengths of the Legs
Find the lengths of a 30-60-90 triangle with
hypotenuse of length 12.
Shorter Leg hypotenuse 2 shorter leg 12
2x x 6
Longer Leg longer leg v3 shorter leg y
xv3 y 6v3
12
Example 9Finding the Lengths of the Legs
Find the lengths of a 30-60-90 triangle with
hypotenuse of length 4v3.
Shorter Leg hypotenuse 2 shorter leg 4v3
2x x 2v3
Longer Leg longer leg v3 shorter leg y
xv3 y 2v3v3 Y6
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Example 10Using the Length of a Leg
Find the value of each variable.
Shorter Leg long leg v3 short leg
Hypotenuse Hyp. 2 shorter leg
5
x
y
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Example 11Using the Length of a Leg
The shorter leg of a 30-60-90 has length v6.
What are the lengths of the other sides? Leave
your answers in simplest radical form.
Longer Leg longer leg v3 shorter leg
Hypotenuse hyp. 2 shorter leg
x
v6
y
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Example 12Using the Length of a Leg
The longer leg of a 30-60-90 has length 18.
Find the length of the shorter leg and the
hypotenuse.
Shorter Leg long leg v3 short leg
Hypotenuse hyp. 2 shorter leg
18
x
y
16
Assignment
Pg. 369 1-29 34-39