Given the diagram at the right, as labeled, find CD.

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2	4

Explanation Altitude Rule: 8/x = x/2 x² = 16 x = 4 (length is positive)

Given the diagram at the right, as labeled, find x.

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8	8.5
9	9.5

Explanation Leg Rule: 6/x = x/13.5 x² = 81 x = 9 (length is positive)

Given the diagram at the right, as labeled, find QR.

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Given the diagram at the right, as labeled,
find x.

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Given the diagram at the right, as labeled,
find x.

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For the diagram shown at the right, which of the following proportions will be always true regarding the segments of the triangle?

In right triangle ΔABC, ∠C is a right angle. , the altitude to the hypotenuse, has a length of 8 units. If the segments of the hypotenuse are in the ratio of 1 : 4, find the number of units in the two segments of the hypotenuse.

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2 and 8

3 and 12

4 and 16

8 and 8

Explanation Let the segments of hypotenuse be x and 4x. Altitude Rule: x/8 = 8/(4x) 4x² = 64 x² = 16 x = 4 and 4x = 16

Given right triangle ΔPQR as shown at the right.
a) Find a.
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The hypotenuse of a right triangle has a length of 50 units, and the longer leg of the triangle has a length of 40 units. What is the length of the projection of the shorter leg on the hypotenuse?

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READ CAREFULLY!
Given the diagram shown at the right, as labeled, find SQ.

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8

12

18

Explanation Need to find x using Leg Rule. (x+10)/12 = 12/x x² + 10x - 144 = 0 (x + 18)(x - 8) = 0 x = 8 Now, use Altitude Rule to find SQ. 10/SQ = SQ/8 (SQ)² = 80 SQ = 4 radical 5

Given a circle labeled as shown with diameter .
AC = 15 cm. and AE = EF = FC.

a) Find CD.
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Challenge Problem: Given right triangle ΔACB with altitude and angle bisector .
Find ED, to nearest hundredth.

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1.32

0.63

0.34

0.26