Special Right Triangles
Warm-Up
December 02, 2014
12/2/14
Find the value of x.
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Special Right Triangles
December 02, 2014
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Special Right Triangles
December 02, 2014
Special Right Triangles
There are two special right triangles which
appear frequently in mathematics. These two
right triangles are named by their angles:
‐the ___________ triangle, and
the __________ triangle.
The 45o-45o-90o Triangle
Consider a square with a diagonal drawn. Given
the length of a side, find the diagonal of the
square.
If the side was 4, then
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Special Right Triangles
December 02, 2014
If the side was 10, then
If the side was 7, then
If a leg is 13, then the hypotenuse is _________.
If a leg is 5, then the hypotenuse is _________.
If a leg is 1/2, then the hypotenuse is _________.
So for a 45o‐45o‐90o triangle, the ratio of a leg to
the hypotenuse is __________.
The ratio of all three sides then:
leg:leg:hypotenuse=
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Special Right Triangles
December 02, 2014
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Special Right Triangles
December 02, 2014
The 30o-60o-90o Triangle
Consider an equilateral triangle with an altitude.
Notice that the altitude divides the equilateral
triangle into two congruent triangles.
Let the short side of one right triangle be x.
Now lets find b in terms of x using Pythagorean
Theorem.
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Special Right Triangles
December 02, 2014
So for a 30o‐60o‐90o triangle, the ratio of the short
leg to the hypotenuse is __________.
For a 30o‐60o‐90o triangle, the ratio of the short
leg to the long leg is __________.
The ratio of all three sides then:
short leg: long leg: hypotenuse=
short leg: hypotenuse: long leg=
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Special Right Triangles
December 02, 2014
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