Question

Can someone solve this?

Answer 1

• See below

Explanation:

Properties of a parallelogram:

• Opposite sides are parallel
• Opposite angles are congruent

We have:

• AB ║ CD
• ∠BAD ≅ ∠BCD

AE is angle bisector of BAD, CF is angle bisector of BCD:

• m∠EAF = 1/2*m∠BAD
• m∠FCE = 1/2*m∠BCD

Since ∠BAD ≅ ∠BCD we also have:

• ∠EAF ≅ ∠FCE
• Also FA ║ CE

It means AFCE is also a parallelogram as opposite angles are congruent and opposite sides are parallel.

Another opposite side pair is also parallel:

• AE ║ CF