Question

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

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

Answer 1

The correct option is C Corresponding angles are equal.

If two parallel lines are intersected by a transversal, we have:

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

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

(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., $\angle 2+\angle 5={180}^{\circ }and\angle 3+\angle 8={180}^{\circ }$.

A line can be constructed parallelly to a given line using any of the above mentioned pairs of angles.

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