contestada

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


Prove: Line DB bisects Angle ABC

Given Line AD is congruent Line CD Angle 3 is congruent to Angle 4Prove Line DB bisects Angle ABC class=

Respuesta :

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,

[tex]\angle3=\angle4\ \{given\}\\\\\implies 180\textdegree-\angle3=180\textdegree-\angle4\\\\\implies\angle 1=\angle 2[/tex]

and

[tex]AD=CD\ \{given\}[/tex]

and

[tex]BD=BD\ \{common\}[/tex]

So, ΔABD ≅ ΔCBD (By SAS criterion}

Hence , By CPCT (corresponding part of congruent triangle}

∠ABD=∠CBD

Therefore, Line DB bisects ∠ABC.

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