Question

Given: Line AD is congruent Line CD; Angle 3 is congruent to Angle 4

Answer 1

Step-by-step explanation:

Given : AD=CD and

           ∠3=∠4

To prove : Line DB bisects ∠ABC

                i.e.∠ABD=∠CBD

Proof :  Consider ΔABD and ΔCBD,

$\angle3=\angle4\ \{given\}\\\\\implies 180\textdegree-\angle3=180\textdegree-\angle4\\\\\implies\angle 1=\angle 2$

and

$AD=CD\ \{given\}$

and

$BD=BD\ \{common\}$

So, ΔABD ≅ ΔCBD (By SAS criterion}

Hence , By CPCT (corresponding part of congruent triangle}

∠ABD=∠CBD

Therefore, Line DB bisects ∠ABC.