Question

Which of the following statements must be true based on the diagram below? (Diagram is not to scale.) D F C B BF is a segment bisector. B is the vertex of a pair of congruent angles in the diagram. F is the vertex of a pair of congruent angles in the diagram. B is the midpoint of a segment in the diagram. F is the midpoint of a segment in the diagram.

Answer 1

Step 1: What is a perpendicular bisector?

A perpendicular bisector can be defined as a line segment that intersects another line perpendicularly and divides it into two equal parts.

Step 2:

We can see from the diagram that line OP divides KL into two equal parts and it is at a right angle to KL, hence, OP is a perpendicular bisector.

Step 3:

O is a midpoint because length OL is equal to the length OK.

Step 4: What is the vertex of the right angle

A vertex of a right triangle is a point where the sides of the triangle meet.

Therefore,

O is a vertex of a right angle

P is a vertex of a right angle

Step 5: Final answer

OP is a perpendicular bisector.

O is a midpoint

O is a vertex of a right angle

P is a vertex of a right angle