Assertion : If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
Reason : If two lines intersect each other, then the vertically opposite angles are equal.
Which of the following is correct

A is true but R is false.

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A is false but R is true.

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Both A and R are true and R is the correct explanation of A.

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Both A and R are true and R is not the correct explanation of A.

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Solution

The correct option is D
Both A and R are true and R is not the correct explanation of A.

Explanation of assertion:
The converse of corresponding angles axiom states that if a transversal intersects two lines such that a pair of corresponding angles are equal, the two lines are parallel to each other.
Explanation of reason:
A pair of vertically opposite angles are always equal. A vertical angle and its adjacent angle are also supplementary angles, which means that they add up to 180 degrees.
The statement in 'Reason' does not prove any assertion of the formation of parallel lines.
Hence, option (D) is the correct answer.

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Similar questions

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.

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 ___

Q. If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.

Assertion : If an angle formed by two intersecting lines is $60^{\circ}$ , then its vertically opposite angle is $60^{\circ}$ .
Reason : If two lines intersect each other, then the vertically opposite angles are equal.

Which of the following is correct.

Q. If two parallel lines are intersected by a transversal, then each pair of corresponding angles are

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Assertion : If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.Reason : If two lines intersect each other, then the vertically opposite angles are equal.Which of the following is correct

Assertion : If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
Reason : If two lines intersect each other, then the vertically opposite angles are equal.
Which of the following is correct