In the figure shown, the two lines are parallel to each other. Which of the following options form a pair of alternate exterior angles?

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Solution

$∠$ 1 and $∠$ 7 form a pair of alternate exterior angles as they are formed on the outer side of the transversal on different sides.
$∠$ 2 and $∠$ 8 form a pair of alternate interior angles, $∠$ 5 and $∠$ 7 form a pair of vertically opposite angles, and $∠$ 1 and $∠$ 5 form a pair of corresponding angles.

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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.

In the figure shown, the two lines are parallel to each other. Which of the following options is incorrect?

Q. Show that the angle bisectors of a pair of alternate angles made by the transversal with two parallel lines are parallel to each other.

Q. Which of the following pair of angles are alternate exterior angles in the given figure?

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In the figure shown, the two lines are parallel to each other. Which of the following options form a pair of alternate exterior angles?

∠1 and ∠7 form a pair of alternate exterior angles as they are formed on the outer side of the transversal on different sides. ∠2 and ∠8 form a pair of alternate interior angles, ∠5 and ∠7 form a pair of vertically opposite angles, and ∠1 and ∠5 form a pair of corresponding angles.