If a transversal intersects two parallel lines, then alternate interior angles are on ____ the side of the transversal.

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Solution

Define alternate angles and identify the alternate angles from the figure
Definition : When a transversal crosses a pair of parallel lines ,the pair of angles formed on the inner side of the parallel lines but on the opposite side of the transversal are called alternate interior angles.
These angles are always equal. From the figure , $1, 4$ are a pair of alternate interior angles.
Hence, the pairs of alternate angles were identified in the opposite side of the transversal from the figure

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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.

Q. When a transversal intersects two non parallel lines, then the alternate interior angles are _____.

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

If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are _______(in degrees).

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