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The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.

Theorem: The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse

longest side across from the right angle

Altitude and Leg Rule

Leg Rule:

piece of hypotenuse that touches the leg

Altitude Rule:

Theorem:Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse

6

16

4

in this example the formula would be X

8

=

4

8

In this case the pieces are the sides

Then you would cross multiply and get 4X=64

4

4X divided by 4=X and 64 divided by 4=16, so the answer would be X=16.

The next example is for the leg rule...

In this case since the leg formula is Hyp=leg

leg

proj

you would get 16=X

12

X

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