When a transversal cuts two lines such that pairs of alternate interior angles are ___, then the lines have to be parallel.

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Solution

When a transversal cuts two lines such that pairs of alternate interior angles are equal, then the lines have to be parallel. The interior alternate angles are always equal for a pair of parallel lines.

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Fill in the blanks in each of the following to make the statement true:
(i) If two parallel lines are intersected by a transversal then each pair of corresponding angles are ___
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ___
(iii) Two lines perpendicular to the same line are ___ to each other.
(iv) Two lines parallel to the same line are to ___ each other.

(v) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ___
(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is $180^{0}$ , then the lines are ___

Q. When two non parallel lines intersect a transversal, the alternate interior angles formed will be ______.

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