Question

In the given figure AB parallel CD and a transversal EF cuts them at G andH

Answer 1

Answer:

We know that

AB∥

CD

and t is a transversal

from the figure we know that∠AEFand∠EFDare alternate angles

So we get

∠AEF= ∠EFD

Dividing both side by 2 we get

2

1

∠AEF=

2

1

∠EFD

So we get

∠PEF= ∠EFQ

The alternate interior angles are formed only when the transversal

EF

cuts both

FQ

and

EP

Therefore it is proved that

EP∥FQ