Question

For the given statements select the correct option.

Assertion : Two lines are parallel if the sum of the co-interior angles made with the transversal is equal to 180°.

Reason : Two distinct lines cannot have more than one point in common

• A. Assertion is true but reason is false.
• B. Assertion is false but reason is true.
• C. Both assertion and reason are true and reason is the correct explanation of assertion.
• D. Both assertion and reason are true but reason is not the correct explanation of assertion.

Answer 1

The correct option is D

Both assertion and reason are true but reason is not the correct explanation of assertion.

Correct Option (B) Both assertion and reason are true but reason is not the correct explanation of assertion.

• This is the property of the parallel lines which can be deduced from the 5th postulate.

• So, the Assertion is correct.

• And, as you may recall, Euclid's first postulate

• A straight line may be drawn from any one point to any other point

• This gives the axiom: Given two distinct points, there is a unique line that passes through them.

• To prove the statement given as the reason:

• For the time being, let us suppose that the two lines intersect in two distinct points, say P and Q.

• So, you have two lines passing through two distinct points P and Q.

• But this assumption clashes with the axiom that only one line can pass through two distinct points.

• So, the assumption that we started with, that two lines can pass through two distinct points is wrong.

• Therefore, We are forced to conclude that two distinct lines cannot have more than one point in common.

• Hence, the Reason is also correct.

• However, Reason is not the proper explanation for the assertion. Because reason fails to articulate Euclid's fifth postulate.