Question

Two distinct __________ in a plane cannot have more than one point in common.

Answer 1

Let p and q be two distinct lines. Suppose these two lines intersect in two distinct point say A and B. So, there are two lines passing through two distinct points A and B. But, this contradicts the axiom that only one line can pass through two distinct points. Hence, our assumption that two lines intersect in two distinct points is wrong. Thus, two distinct lines cannot have more than one point in common.

Two distinct __lines__ in a plane cannot have more than one point in common.