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Question

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

A

Alternate interior angles are supplementary.

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B

Co-interior angles are equal.

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C

Vertically opposite angles are equal.

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D

Corresponding angles are equal.

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Solution

## The correct option is D Corresponding angles are equal. If two parallel lines are intersected by a transversal: (i) alternate interior angles are equal i.e., 2=8 and 3=5 (ii) alternate exterior angles are equal i.e., 1=7 and 4=6 (iii) corresponding angles are equal i.e., 1=5,4=8,2=6 and 3=7 (iv) co-interior angles are supplementary i.e., 2+5=180∘ and 3+8=180∘ 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.

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