4. In a right-angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Home » 4. In a right-angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

4. In a right-angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Given : Consider ΔABC to be a right angle triangle having sides a, b and hypotenuse c. Let BD be the altitude drawn on the hypotenuse AC.

To prove: ab = cx

Prove :

In ΔACB and ΔCDB

∠B = ∠B (Common)

$∠ACB = ∠CDB = 90<sup>o</sup>$

(By AA similarity criteria)

⇒ ΔACB ∼ ΔCDB

(Corresponding Parts of Similar Triangles are propositional)

AB/ BD = AC/ BC

a/ x = c/ b

⇒ xc = ab

ab = cx

Hence, proved.

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