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 2 out of 2 (overline{oq}) is a segment bisector. (q) is the vertex of two angles that are congruent to one another. (q) is the vertex of a right angle. (o) is the midpoint of a segment in the diagram. (q) is the midpoint of a segment in the diagram. none of the above.

Explanation:

1. For "\(\overline{OQ}\) is a segment bisector": In the diagram, \(\overline{OQ}\) splits the angles at \(O\) and \(Q\) (marked with congruent angle marks), and likely bisects the segments \(RP\) (if we consider the rhombus - like figure, diagonals bisect each other and bisect the angles). So \(\overline{OQ}\) can be a segment bisector of \(RP\), so this statement can be true.
2. For " \(Q\) is the vertex of two angles that are congruent to one another": The angle marks at \(Q\) show that the two angles with vertex \(Q\) (formed by \(\overline{OQ}\) and the other sides) are congruent (marked with the same number of tick marks), so \(Q\) is the vertex of two congruent angles. This statement is true.
3. For " \(Q\) is the vertex of a right angle": There is no indication (like a right - angle symbol or information) that the angle at \(Q\) is a right angle. So this statement is false.
4. For " \(O\) is the midpoint of a segment in the diagram": There is no segment shown with \(O\) as its midpoint. The segment \(\overline{OQ}\) has \(O\) at one end, not as a midpoint. So this statement is false.
5. For " \(Q\) is the midpoint of a segment in the diagram": In the diagram, \(Q\) is an endpoint of \(\overline{OQ}\), not a midpoint of any segment. So this statement is false.

Answer:

• \(\boldsymbol{\overline{OQ}}\) is a segment bisector.
• \(\boldsymbol{Q}\) is the vertex of two angles that are congruent to one another.