Question

Which of the following statements is NOT true for perpendicular bisectors?

a. Perpendicular bisectors split the side of the triangle into two congruent segments.
b. Perpendicular bisectors form a right angle at the vertex of the triangle.
c. Perpendicular bisectors form a right angle with the side of the triangle it is bisecting.
d. Perpendicular bisectors intersect the side of the triangle at the midpoint of the side.

Answer 1

The statement that is NOT true for perpendicular bisectors is: option b). Perpendicular bisectors form a right angle at the vertex of the triangle.

Step-by-step explanation:

A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point. Thus, we can say, a perpendicular bisector always divides a line segment through its midpoint.

The statement that is NOT true for perpendicular bisectors is: b). Perpendicular bisectors form a right angle at the vertex of the triangle.

This is incorrect because a perpendicular bisector intersects the midpoint of a side of a triangle and does not necessarily intersect at the vertex unless it's also a median. The other statements are true for perpendicular bisectors:

• a. Perpendicular bisectors split the side of the triangle into two congruent segments: This is true as the definition of a bisector is to divide the side into two equal parts.
• c. Perpendicular bisectors form a right angle with the side of the triangle it is bisecting: Also true, as 'perpendicular' implies a 90° angle.
• d. Perpendicular bisectors intersect the side of the triangle at the midpoint of the side: True, because a 'bisector' by definition intersects at the midpoint.