Question

Bisector / Midpoint/Vertex on DiagramJol 28, 10:36:34 AM?Which of the following statements must be true based on the diagram below?(Diagram is not to scale.)PRRS is a segment bisector.ORS is a perpendicular bisector.oS is the vertex of a pair of congruent angles in the diagram.o R is the midpoint of a segment in the diagram.S is the midpoint of a segment in the diagram.None of the above.

Answer 1

From the figure in the question,

Since PR = RQ, Then

The line RS divides the line segment PQ into two equal halves

Hence

$\bar{RS}\text{ is a segment bisector}$

Also, the angle at R is 90 degree

Therefore line RS is perpendicular to line PQ

Hence

$\bar{RS}\text{ is a perpendicular bisector}$

Also,

since PR = RQ

Then, R is the mid-point of PQ

Hence

$R\text{ is the midpoint of a segment in the diagram}$

Therefore

The following are the corrcet answers

1. Line RS is a segment bisector

2. Line RS is a perpendicular bisector

3. R is the midpoint of a segment in the diagram