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Always true. To see this draw the circle which passes through the three points of the triangle. Reproduce the reflection of the triangle on the hypotenuse (which passes through the centre). Then use the theorem of intersecting chords of a circle to give the result immediately. It's also simply proved by algebra.

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Q: What if the altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse?
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Related questions

What is the length of the altitude to the hypotenuse in a right triangle if this altitude divides the hypotenuse into segments of lengths 8 millimeters and 18 millimeters?

What a neat little problem ! I'll remember this one, and I'll use it. The altitude to the hypotenuse is 12.0 millimeters long.


What is the altitude of a right triangle if the base is 96 and the hypotenuse is 240?

The altitude of a right triangle if the base is 96 and the hypotenuse is 240 is: 229.87


What is the formula to find the altitude to the hypotenuse of a right triangle?

It is: c2-b2 = a2 whereas c is the hypotenuse, b is the base and a is the altitude


How do you find the altitude of the hypotenuse in a right triangle?

By using Pythagoras' theorem: hypotenuse^2 minus base^2 = altitude^2


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True, because the slant height and the altitude, or height, of the pyramid form one leg and the hypotenuse of a triangle withing the pyramid, and the hypotenuse of a triangle is always the longest side- it is not possible for the hypotenuse to be equal to the legs of a right triangle. (It is a right triangle because an altitude is perpendicular to the base of a pyramid.)


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