are the angles which lie inside of the two parallel lines but on alternate sides of the transversal.

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Solution

Alternate interior angles are the angles that lie inside of the two parallel lines but on alternate sides of the transversal.
For example,

here, $∠ A P F$ and $∠ E O D$ lie on the inside of the two parallel lines AB and CD.
Also, these angles are on alternate side of the transversal EF.

$∠ A P F$ and $∠ E O D$ are alternate interior angles.
Similiarly, $∠ B P F & ∠ E O C$ are alternate interior angles.

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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.
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Q. The alternate interior angles are congruent when the transversal intersects two parallel lines.

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