Question

for each statement, choose whether it is always, sometimes, or never true.

part 1 of 3

(a) there are at least two distinct lines through points ( j ) and ( k ).

part 2 of 3

(b) the intersection of two distinct lines is a point.

Explanation:

Part (a)

Step1: Recall the postulate

According to the postulate, through two distinct points, there is exactly one line.

Step2: Analyze the statement

If there is exactly one line through two distinct points \(J\) and \(K\), then having at least two distinct lines through \(J\) and \(K\) is impossible.

Part (b)

Step1: Consider different cases of lines

In a plane, two distinct lines can be either intersecting or parallel.

Step2: Analyze the intersection

When two distinct lines are not parallel, they intersect at a point. But when two distinct lines are parallel, they do not intersect. So the statement “The intersection of two distinct lines is a point” is not always true.

Answer:

(a) Never true
(b) Sometimes true