Question

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles, so formed are parallel

Answer 1

Please refer to the attached image..






Hope it helps

Answer 2

$\huge\underline\mathbb\blue{ANSWER}$

Given:

$AB || CD$

To Prove:

$\angle{MPA} = \angle{ PQC}$

Proof:⏩

We know that

$\angle{MPA} = \angle{BPQ}$

{vertically opposite angles} ...(1)

Also,

$\angle{ BPQ} = \angle{ PQC}$

{alternate interior angles}...(2)

From (1) and (2),

→ Things equal to the same things are equal to each other.

Thus,

$\huge\mathbb{\angle{MPA} = \angle{ PQC}}$

hope it's helpful ✅✅✅