Q. 53.7( 3 Votes )

In ΔABC if B = 90° and BD perpendicular to hypotenuse AC then prove that ΔADB ~ ΔBDC.

Answer :


Let ABD = x


⇒ ∠BAD = 90 – x


DBC = 90 – x


DCB = 90 – (90 – x) = x


In ΔADB&ΔBDC,


ADB = BDC = 90°


ABD = DCB = x


BAD = DBC = 90 – x


ΔADB~ΔBDC by AAA Similarity Rule


Hence, proved.


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