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Question

Four points are plotted on the circumference of a circle and are joined by line segments.

Which of the following statements is true?

(1 point)
Responses

∠FDG≅∠DFE
angle upper F upper D upper G congruent to angle upper D upper F upper E

∠FEG≅∠FDG
angle upper F upper E upper G congruent to angle upper F upper D upper G

∠GDF≅∠DGE
angle upper G upper D upper F congruent to angle upper D upper G upper E

∠DFE≅∠GEF

Answer 1

To answer the question regarding the angles formed by four points on the circumference of a circle, we need to recall a few properties of circles and angles.

When four points are on a circle, the angles formed by the segments connecting these points can be assessed using the Inscribed Angle Theorem. This theorem states that the inscribed angle is half the measure of the intercepted arc.

Let's analyze the choices one by one:

1. ∠FDG≅∠DFE: This statement compares angles that are not likely to be equal unless specific points coincide, which they do not based on typical circular geometry.

2. ∠FEG≅∠FDG: Again, these angles relate to different arcs and would not generally be equal.

3. ∠GDF≅∠DGE: This could potentially be true if angles correspond to similar arcs, but without specific information about the placement of points G, D, and E, we cannot confirm this as true in a general sense.

4. ∠DFE≅∠GEF: This is a strong contender because both angles share point D and relate to the arcs GF and DE, respectively. By properties of angles inscribed in the same segment, this relationship can hold valid.

Given these statements and properties of angles in circles, the most likely correct answer is:

∠DFE≅∠GEF