Question

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Answer 1

Question :

• Prove that the bisectors of a pair of alternate interior angles are parallel.

Given :

• AB || CD
• PQ is the transversal
• MX and NX respectively bisect ∠CMN and ∠BMN

To Prove :

• MY || NX

Solution :

᠂․᠂ AB || CD

Therefore, ∠CMN = ∠BNM (Alternate interior angles)

Now,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf \longrightarrow \dfrac{\angle CMN}{2} \: = \dfrac{\angle BNM}{2} \\ \\ \\ \sf \: \longrightarrow \: \angle YMN \: = \: \angle MNX$

᠂․᠂ Alternate interior angles ∠YMN and ∠MNX are equal.

• Alternate interior angles are equal when the lines are equal.

Therefore, MY || NX.

Hence, Proved!