5-8 Applying Special Right Triangles
Objectives
Justify and apply properties of
45°-45°-90° triangles.
Justify and apply properties of
30°- 60°- 90° triangles.
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5-8 Applying Special Right Triangles
A diagonal of a square divides it into two congruent
isosceles right triangles. Since the base angles of an
isosceles triangle are congruent, the measure of
each acute angle is 45°. So another name for an
isosceles right triangle is a 45°-45°-90° triangle.
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5-8 Applying Special Right Triangles
Holt Geometry
5-8 Applying Special Right Triangles
Example 1A: Finding Side Lengths in a 45°- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
By the Triangle Sum Theorem, the
measure of the third angle in the
triangle is 45°. So it is a 45°-45°90° triangle with a leg length of 8.
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5-8 Applying Special Right Triangles
Example 1B: Finding Side Lengths in a 45º- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
The triangle is an isosceles right
triangle, which is a 45°-45°-90°
triangle. The length of the hypotenuse
is 5.
Rationalize the denominator.
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5-8 Applying Special Right Triangles
Example 1c
Find the value of x. Give your answer in
simplest radical form.
By the Triangle Sum Theorem, the
measure of the third angle in the
triangle is 45°. So it is a 45°-45°90° triangle with a leg length of
x = 20
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Simplify.
5-8 Applying Special Right Triangles
Example 1d
Find the value of x. Give your answer in
simplest radical form.
The triangle is an isosceles right
triangle, which is a 45°-45°-90°
triangle. The length of the
hypotenuse is 16.
Rationalize the denominator.
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5-8 Applying Special Right Triangles
A 30°-60°-90° triangle is another special right
triangle. You can use an equilateral triangle to find
a relationship between its side lengths.
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5-8 Applying Special Right Triangles
Example 2A: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y. Give
your answers in simplest
radical form.
22 = 2x
Hypotenuse = 2(shorter leg)
11 = x
Divide both sides by 2.
Substitute 11 for x.
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5-8 Applying Special Right Triangles
Example 2B: Finding Side Lengths in a 30º-60º-90º
Triangle
Find the values of x and y. Give your
answers in simplest radical form.
Rationalize the denominator.
y = 2x
Hypotenuse = 2(shorter leg).
Simplify.
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5-8 Applying Special Right Triangles
Example 2c
Find the values of x and y.
Give your answers in simplest
radical form.
Hypotenuse = 2(shorter leg)
Divide both sides by 2.
y = 27
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Substitute
for x.
5-8 Applying Special Right Triangles
Check It Out! Example 2d
Find the values of x and y.
Give your answers in
simplest radical form.
y = 2(5)
y = 10
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Simplify.
5-8 Applying Special Right Triangles
Lesson Quiz: Part I
Find the values of the variables. Give your
answers in simplest radical form.
1.
2.
x = 10; y = 20
3.
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4.
5-8 Applying Special Right Triangles
Lesson Quiz: Part II
Find the perimeter and area of each figure.
Give your answers in simplest radical form.
5. a square with diagonal length 20 cm
6. an equilateral triangle with height 24 in.
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