Question

if two distinct lines intersect, which is not necessarily true?
a the lines are not parallel.
b the lines are perpendicular.
c the lines form angles at the intersection.
d the intersection of the two lines is a point.

Explanation:

Step1: Analyze Option A

By the definition of parallel lines (they do not intersect), if two distinct lines intersect, they are not parallel.

Step2: Analyze Option B

Two intersecting lines are perpendicular only if the angle between them is \(90^{\circ}\). But just because two lines intersect doesn't mean the angle between them is \(90^{\circ}\).

Step3: Analyze Option C

When two lines intersect, they form angles at the intersection point (vertically - opposite angles, adjacent angles etc.).

Step4: Analyze Option D

By the basic property of lines in a plane, the intersection of two distinct lines is a single point.

Answer:

B. The lines are perpendicular.