Answer :

**Given: **In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x.**To prove: **ab = cx**Proof:**

Let in a right-angled triangle ABC at B, a perpendicular from C to AB is drawn such that

BC = a

AC = b

BA = c

BD = x

In ΔABC and ΔCDB

∠B = ∠B (Common)

∠ABC = ∠CDB (Both 90°)

Then, ΔABC ~ ΔCDB (By AA Similarity)

So, (Corresponding parts of similar triangle area proportion)

Or

Or ab = cx

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