Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)

answer choices:
dg is a perpendicular bisector.
g is the vertex of two angles that are congruent to one another.
d is the vertex of a right angle.
d is the midpoint of a segment in the diagram.
g is the midpoint of a segment in the diagram.
none of the above

Explanation:

1. For "DG is a perpendicular bisector": A perpendicular bisector must be perpendicular (form a right angle) and bisect a segment. The diagram only shows DG as a segment from D to G on EC, with DE perpendicular to EC (since angle at E looks right, but DG isn't shown as perpendicular to EC or bisecting a segment into two equal parts. So this is not necessarily true.
2. For "G is the vertex of two angles that are congruent to one another": There's no indication (like markings or given info) that angles at G are congruent. So not necessarily true.
3. For "D is the vertex of a right angle": The right angle seems to be at E (DE perpendicular to EC), not at D. So D is not the vertex of a right angle here.
4. For "D is the midpoint of a segment in the diagram": There's no segment shown with D as its midpoint. The segments are DE, DG, DC, EC. D is an endpoint, not a midpoint.
5. For "G is the midpoint of a segment in the diagram": There's no indication (like equal segment markings) that G bisects EC or any other segment. So not necessarily true.

Since none of the statements must be true based on the diagram (which is not to scale and has no markings for congruence, midpoints, or perpendicular bisectors), the correct option is "None of the above".

Answer:

None of the above