Question

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

diagram: triangle with vertex d at the top, and points e, g, c on the base (e---g---c), with segments de, dg, dc drawn from d to each base point.

answer choices:

• ( overline{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 doesn't show DG as perpendicular or bisecting a segment, so this is false.
2. For "G is the vertex of two angles that are congruent to one another": There's no indication (like markings) that angles at G are congruent, so this is false.
3. For "D is the vertex of a right angle": The diagram doesn't show a right angle at D, so this is false.
4. For "D is the midpoint of a segment in the diagram": D is a vertex, not a midpoint of any segment shown, so this is false.
5. For "G is the midpoint of a segment in the diagram": There's no indication (like markings) that G bisects EC, so this is false.

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

Answer:

None of the above.