Which of the following statements are true (T) 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.
Answers
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
FALSE
Reason: If a transversal intersects two PARALLEL LINES then each pair of corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
TRUE
Reason : If a transversal intersects two PARALLEL LINES then each pair of alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
FALSE
Reason : Two lines perpendicular to the same line are PARALLEL to each other.
(iv) Two lines parallel to the same line are parallel to each other.
TRUE
Reason : 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.
FALSE
Reason : If a transversal intersects two PARALLEL LINES then each pair of the interior angles on the same side are supplementary (180°).
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(iii) Two lines perpendicular to the same line are …….. to each other.
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(i) If two lines are intersected by a transversal, then corresponding angles are equal.
The sentence is False.
Reason: The lines which are intersected by the transversal need to be parallel to each other in order to the corresponding angles be equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
The sentence is True.
Reason: The pair of alternate angles formed on the intersection of transdermal to a pair of parallel lines are always equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
The sentence is False.
Reason: The lines are parallel to each other, and not perpendicular.
(iv) Two lines parallel to the same line are parallel to each other.
The sentence is True.
Reason: If two lines are parallel to each other, then any line parallel to any one of them is parallel to both the lines.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.
The sentence is False.
Reason: The angles are supplementary, and not equal.