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AAA Similarity

In a right an...

Question

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

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Solution

In ABC and ADB
ABC = ADB (right angle)
BAD = BAC (common angle)

Both the triangles are similar by AA similarity criteria
So,
$fraction numerator A B over denominator A C end fraction equals fraction numerator B D over denominator B C end fraction a over c equals x over b a b equals c x H e n c e space p r o v e d$

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