To determine which statements must be true based on the diagram (which unfortunately I cannot see), we need to analyze the given statements conceptually. Let’s review the statements based on common geometric principles:
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G is the vertex of a pair of congruent angles in the diagram.
- This statement can be true if it is indicated that angles formed at G are equal. However, without seeing the diagram, we cannot confirm this.
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EG is a segment bisector.
- A segment bisector divides a segment into two equal parts. If the diagram indicates EG bisects another segment at its midpoint, this would be true.
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E is the vertex of a pair of congruent angles in the diagram.
- Similar to the first statement, this can be true only if the angles at E are shown to be equal in the diagram.
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G is the midpoint of a segment in the diagram.
- This statement would hold true if G is indicated as dividing a segment into two equal parts.
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E is the midpoint of a segment in the diagram.
- This could be true if E is specified to divide another segment equally.
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EG is an angle bisector.
- An angle bisector divides an angle into two equal angles. If EG is shown to do this in the diagram, then the statement is true.
To accurately determine which statements are true, you would need to look for indications in the diagram, such as markings showing equal angles or midpoints.
Based on the diagram's details, confirm which statements relate to angle congruence or segment bisection visually to select those that are definitely true. If there are no specific marks or indications supporting the statements, you cannot claim them to be universally true without additional context.
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