Name _______________________________________ Date ___________________ Class __________________
Section 5.8
Applying Special Right Triangles
Theorem
Example
458-458-908 Triangle Theorem
In a 458-458-908 triangle, both legs are
congruent and the length of the hypotenuse
is 2 times the length of a leg.
In a 458-458-908 triangle, if a leg
length is x, then the hypotenuse
length is x 2.
Use the 458-458-908 Triangle Theorem to find the value of x inEFG.
Every isosceles right triangle is a 458-458-908 triangle. Triangle
EFG is a 458-458-908 triangle with a hypotenuse of length 10.
10  x 2
10
2

x 2
5 2x
2
Hypotenuse is
2 times the length of a leg.
Divide both sides by
2.
Rationalize the denominator.
Find the value of x. Give your answers in simplest radical form.
1.
2.
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3.
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4.
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Section 5.8
Applying Special Right Triangles continued
Theorem
Examples
308-608-908 Triangle Theorem
In a 308-608-908 triangle, the length of the
hypotenuse is 2 multiplied by the length of
the shorter leg, and the longer leg is 3
multiplied by the length of the shorter leg.
In a 308-608-908 triangle, if the shorter leg
length is x, then the hypotenuse length
is 2x and the longer leg length is x.
Use the 308-608-908 Triangle Theorem to find the values
of x and y inHJK.
12  x 3
12
3
x
4 3x
Longer leg  shorter leg multiplied by
Divide both sides by
3.
3.
Rationalize the denominator.
y  2x
Hypotenuse  2 multiplied by shorter leg.
y  2(4 3)
Substitute 4 3 for x.
y 8 3
Simplify.
Find the values of x and y. Give your answers in simplest radical
form.
5.
6.
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7.
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8.
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Section 5.8
1. x  17 2
2. x  22 2
3. x  4 2
4. x  25
5. x  9; y  9 3
6. x  2 3 ; y  4
7. x  12 3 ; y  36
8. x  11 3 ; y  22 3
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry