Question

Preeti told Pavani that if the alternate interior angles are equal then lines need not be parallel. Is Preeti's statement true or false?

• A. True
• B. False

Answer 1

The correct option is B

False

If two parallel lines are intersected by a transversal:

(i) alternate interior angles are equal i.e., $\angle$2=$\angle$8 and $\angle$3=$\angle$5

(ii) alternate exterior angles are equal i.e., $\angle$1=$\angle$7 and $\angle$4=$\angle$6

(iii) corresponding angles are equal i.e., $\angle$1=$\angle$5,$\angle$4=$\angle$8,$\angle$2=$\angle$6 and $\angle$3=$\angle$7

(iv) co-interior angles are supplementary i.e., $\angle$2 +$\angle$5= ${180}^{\circ }and\angle$3 +$\angle$8 =${180}^{\circ }$.

Hence, if the alternate angles are equal then the lines are parallel.