Question

In AABC, 2B = 90° and D is a point on AC such that
DBC = ZDCB. Prove that BD = AD.​

Answer 1

Step-by-step explanation:

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