If a transversal intersects two parallel lines, then corresponding angles are on the _____ side of the transversal.

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Solution

Define corresponding angles and understand their position with respect to the transversal
Definition: When a transversal cuts a pair of parallel lines, the angles that occupy the same relative position at the intersection are called as corresponding angles. Corresponding angles are always equal
From the figure we can see
$∠ 6$ is corresponding to $∠ 2$
$∠ 5$ is corresponding to $∠ 1$
$∠ 7$ is corresponding to $∠ 3$
$∠ 8$ is corresponding to $∠ 4$
Hence as their relative position is same, they are on the same side of the transversal.

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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 ___

Which of the following statements are true (I) and which are false (F)? Give reasons.
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two lines parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

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(iv) If AB is a line and P is a point outside it then how many lines can be drawn through P and Parallel to AB?
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What happens to the corresponding angles when a transversal intersect a non- parallel lines?

Q. If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

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