Question

question which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.) 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 to a segment and bisect it. The diagram only shows DG as a segment from D to G on EC, with no indication of perpendicularity or bisecting (no right angle mark or G being midpoint shown), so this is false.
2. For "G is the vertex of two angles that are congruent to one another": There's no marking (like arcs) to show angle congruence at G, so we can't assume this, false.
3. For "D is the vertex of a right angle": There's no right angle symbol at D, so we can't conclude D is a right angle vertex, false.
4. For "D is the midpoint of a segment in the diagram": D is a vertex connected to E, G, C; no segment has D as midpoint (midpoint would be equidistant, no such indication), false.
5. For "G is the midpoint of a segment in the diagram": The diagram doesn't show EG = GC (no midpoint marking), so we can't say G is a midpoint, false.

Since all other options are false, the correct answer is "None of the above".

Answer:

None of the above.