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in triangle abc ,angle b =90°d is hypotenuse ac such that angle dbc = angle dcb.prove that ad=bd

Posted by Sahil Kumar 5 years ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 5 years ago

In ∆ABC , angle B=90° and D is a point on hypotenuse AC such that angle DBC

= angle DCB.

In,∆ABC. let angle ACB or DCB = x° , then angle BAC or BAD = 90°-x………..(1)

In. ∆ DBC angle DBC= angle DCB=x°………..(given)

But angle ABD+angle DBC =90°

or. angle ABD. = 90°-x°……………(2)

from eqn. (1) and (2)

angle BAD =angle ABD…….(In ∆ DAB opposite angles are equal ,then opposite

sides are also equal.)

Thus , side BD = side AD. Proved.

1Thank You

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CBSE > Class 09 > Mathematics