The altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse.
A.)always
B.)sometimes
C.)never

If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Let ΔABC with ∠B = 90° and BD ⊥ AC

from above result,

ΔABD is similar to ΔCBD

[tex]\implies\frac{AD}{BD}=\frac{BD}{CD}=\frac{AB}{CB}[/tex]

considering first equality we get,

BD² = AD . CD

This Proves that the altitude to the hypotenuse of a right triangle is always the geometric mean between the segments on the hypotenuse.

.

Therefore, Option A is correct.

The altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse. A.)always B.)sometimes C.)never

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The altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse.
A.)always
B.)sometimes
C.)never