The right triangle altitude theorem - practice problems - last page
The altitude to the hypotenuse is the geometric mean of the two segments of the hypotenuse. Each leg of the right triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.h=c1c2
Also known as a geometric mean theorem. The geometric mean theorem is a special case of the chord theorem.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 64
- The bridge
Across the circle, the lake passes through its center bridge over the lake. At three different locations on the lakeshore are three fishermen, A, B, and C. Which of the fishermen see the bridge from the largest angle? - Construct 61253
Using Euclid's theorem, construct a line of length √15. - Same area
There is a given triangle. Construct a square of the same area. - Conical area
A right-angled triangle has sides a=12 and b=19 at the right angle. The hypotenuse is c. If the triangle rotates on the c side as an axis, find the volume and surface area of the conical area created by this rotation.
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