Question

Which of the given concepts can be used for the construction of a line parallel to the given line?

• A. Vertically opposite angles are equal.
• B. Corresponding angles are equal.
• C. Co-interior angles are equal.
• D. Alternate interior angles are supplementary.

Answer 1

The correct option is B

Corresponding angles are equal.

If two parallel lines are intersected by a transversal:

(i) alternate interior angles are equal i.e., $2=8and3=5$

(ii) alternate exterior angles are equal i.e., $1=7and4=6$

(iii) corresponding angles are equal i.e., $1=5,4=8,2=6and3=7$

(iv) co-interior angles are supplementary i.e., $2+5={180}^{\circ }and3+8={180}^{\circ }$

A line can be constructed parallel to a given line by making any of the above mentioned pairs of angles equal.

Hence, using the equal corresponding angles concept, parallel lines can be constructed.