8-4%20Special%20Right%20Triangles

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8-4 Special Right Triangles
One of the most important topics covered in
geometry

• -45-45-90
• -30-60-90

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45-45-90
Theorem in a 45-45-90 triangle, the hypotenuse
is times as long as a leg.
In basic terms, this means that both legs of a
45-45-90 triangle are congruent, because it is
isosceles. And the hypotenuse is whatever a leg
is multiplied by
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45-45-90 Template
My word of advice This is one of the most
important things you will take from geometry,
MEMORIZE THIS TEMPLATE AND KNOW HOW TO USE IT
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Practice
Every time that you use a special right triangle,
it is helpful to draw the template next to the
triangle you are working with. It is helpful if
they are in the same orientation too.
Find the missing side lengths
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If you are given the side of a 45-45-90 triangle
you simply find the hypotenuse by multiplying by
If given the hypotenuse, to find the legs, you
simply divide the hypotenuse by
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Find both missing side lengths
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Find the missing side lengths
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30-60-90
Theorem In a 30-60-90 right triangle, the
hypotenuse is twice as long as the shortest leg,
and the longest legs is times as long
as the shortest leg
Which angle is the smallest? 30, 60, or 90?
So what side is the smallest? That is enough
information to reconstruct the 30-60-90 template.
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Given the side opposite the 30 angle.
-Double it to find the hypotenuse -Multiply
it by to find the other leg.
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Given the side opposite the 90 angle.
-Divide it by 2 to find the side opposite the
30 angle (shortest side). -Multiply the
shortest side by to find the other leg.
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Case 1
Given the side opposite the 60 angle. Case 1
Given with a -then use the
constant in front to use as your side opposite
your 30 angle. -multiply the shortest side by
2 then to get the hypotenuse.
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Case 2
Given the side opposite the 60 angle. Case 2
Given the length without a -then you divide
that side by to find what your shortest
side is. -multiply the shortest side by 2 then
to get the hypotenuse.
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