Question

Writing two column proofs Given: BC bisects. ABD M ABD =52° prove: mABC=26°

Answer 1

Given

BC bisects ABD

∠ ABD =52°

prove: m ∠ABC=26°

To proof

As given in the question

BC bisects ∠ABD

This means BC divided ∠ABD into the two equal parts.

Therefore

$\angle ABC = \frac{1}{2}\angle ABD$

As given

∠ABD = 52°

put this in the above value

we get

$\angle ABC =\frac{1}{2}52^{\circ}$

∠ABC = 26°

Hence proved

 

Answer 2

Answer with explanation:

Given : It is given that, In Δ ABD,  BC bisects ∠ABD.

To Prove : m ∠ABC=26°

Proof:

   In ΔABD, BC bisects, ∠ABD.

The Meaning of Bisecting an Angle is to divide that Angle is into two Equal parts.

So, ∠ABC=∠DBC------(1)

∠ABD=52°

→∠ABC+∠DBC=52°

→2∠ABC=52°-----[Using 1 ]

Dividing both sides by, 2 we get

→∠ABC=26°

Hence Proved.