Question

In ΔABC,
AD =DC=BD.prove that
LABC= 90°​

Answer 1

${\underline{\underline{\huge{\red{\sf{Answer:-}}}}}}$

${\underline{\underline{Given:-}}}$

AD = BD = CD

${\underline{\underline{To \:Prove:-}}}$

angle ABC = 90°

${\underline{\underline{Proof:-}}}$

Consider the triangle in the attachment.

In ∆ABD,

BD = AD

=> angle 1 = angle 2 ___(2)____(Angles opposite equal sides are equal)

In ∆BDC,

BD = DC

=> angle 3 = angle 4 ___(1)____(Angles opposite equal sides are equal)

In ∆ABC,

angle 1 + angle ABC + angle 4 = 180° ___(Angle Sum Property)

=> angle 1 + angle 2 + angle 3 + angle 4 = 180°

=> angle 2 + angle 2 + angle 3 + angle 3 = 180° ______(Since (1) and (2))

=> 2(angle 2 + angle 3) = 180°

=> angle 2 + angle 3 = 180° ÷ 2

=> angle 2 + angle 3 = 90°

=> angle ABC = 90°

${\underline{\underline{\red{Hence,\: Proved}}}}$