A perpendicular line passing through two parallel lines is a transversal.

True

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False

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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.

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. (i) If a transversal intersects two parallel lines then state the relation between alternate angles.
(ii) If each of the two parallel lines are parallel to the third line then what is the relation between them?
(iii) If a transversal intersects two parallel lines and the corresponding sides of two angles are parallel then what is the relation between these angles?
(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?
(v) If a transversal intersects two parallel lines such that the ratio between the interior angles on one of its side is 2:7, then find the measure of the greater angle.

A perpendicular line passing through two parallel lines is a transversal.

(a) There are two sets of parallel lines passing through a plane. A transversal cuts the two sets of lines. Find the number of distinct points of intersection.

(b) The following diagram shows parallel lines cut by a transversal. Find x. [3 MARKS]

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