Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)
answer attempt 1 out of 2
\\(overline{rt}\\) is a perpendicular bisector.

Explanation:

To determine if \(\overline{RT}\) is a perpendicular bisector, we analyze the diagram:

1. A perpendicular bisector of a segment must:

• Bisect the segment (divide it into two equal parts).
• Be perpendicular to the segment (form a \(90^\circ\) angle with it).

1. From the diagram, \(\overline{RT}\) splits \(\overline{QP}\) at \(T\), but there is no indication (e.g., right - angle symbol, equal - length markings for the bisected segment) that \(\overline{RT}\) is perpendicular to \(\overline{QP}\) or that it bisects \(\overline{QP}\) (or any other segment) in the required way for a perpendicular bisector. The markings at \(R\) only show angle - bisecting, not perpendicularity or bisecting of a segment by \(\overline{RT}\).

So, the statement “\(\overline{RT}\) is a perpendicular bisector” is false.

Answer:

To determine if \(\overline{RT}\) is a perpendicular bisector, we analyze the diagram:

1. A perpendicular bisector of a segment must:

• Bisect the segment (divide it into two equal parts).
• Be perpendicular to the segment (form a \(90^\circ\) angle with it).

1. From the diagram, \(\overline{RT}\) splits \(\overline{QP}\) at \(T\), but there is no indication (e.g., right - angle symbol, equal - length markings for the bisected segment) that \(\overline{RT}\) is perpendicular to \(\overline{QP}\) or that it bisects \(\overline{QP}\) (or any other segment) in the required way for a perpendicular bisector. The markings at \(R\) only show angle - bisecting, not perpendicularity or bisecting of a segment by \(\overline{RT}\).

So, the statement “\(\overline{RT}\) is a perpendicular bisector” is false.