Question

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

Prove: Line DB bisects Angle ABC

Answer 1

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.