If two parallel lines are cut by a transversal then each pair of alternate interior angles are _______.

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Solution

Whenever two parallel lines are cut by a transversal,
Pairs of alternate interior angles $(∠ 2, ∠ 8) a n d (∠ 3, ∠ 5)$ are equal.

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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.

Write converses of the following statements.

(i) The alternate angles formed by two parallel lines and their transversal are congruent.

(ii) If a pair of the interior angles made by a transversal of two lines are supplementary then the lines are parallel.

(iii) The diagonals of a rectangle are congruent.

If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:

If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

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If two parallel lines are cut by a transversal then each pair of alternate interior angles are _______.

Whenever two parallel lines are cut by a transversal, Pairs of alternate interior angles (∠2,∠8)and(∠3,∠5) are equal.

Whenever two parallel lines are cut by a transversal,
Pairs of alternate interior angles $(∠ 2, ∠ 8) a n d (∠ 3, ∠ 5)$ are equal.