If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are_______.

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Solution

The lines would be parallel because pair of alternate angles are equal for two lines which are parallel.

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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 ___

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When a transversal cuts two lines such that pairs of alternate interior angles are equal, then the lines are

Q. If a transversal intersects two parallel lines then show that the bisectors of any pair of alternate angles are also parallel.

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