Question

To prove that AB||EF in the given figure​

Answer 1

Answer:

We have

angle DCB = angle DCF + angle FCB

=angle DCB = ABC

But, angle DCB and angle ABC are alternate interior angles.

Thus,ABIICD

Again angle DCF + angle CFE=30°+ 150°=180°

But,angle DCF and angle CFE are co-interior angles.

Thus,CDIIFE

From (i) and (ii) we get ABIICDIIEF

Hence, ABIIEF

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Answer 2

Answer:

We have

angle DCB = angle DCF + angle FCB

=angle DCB = ABC

But, angle DCB and angle ABC are alternate interior angles.

Thus, ABIICD

Again angle DCF + angle CFE=30°+ 150°=180°

But, angle DCF and angle CFE are co-interior angles.

Thus, CDIIFE

From (i) and (ii) we get ABIICDIIEF

Hence, ABIIEF

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