Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)
A
B
C
D
An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-N for Nemeth.
Answer
 start overline, C, D, end overline 
CD
  is a perpendicular bisector.
 start overline, C, D, end overline 
CD
  is an angle bisector.
 CC is the vertex of a pair of congruent angles in the diagram.
 CC is the vertex of a right angle.
 CC is the midpoint of a segment in the diagram.
 DD is the midpoint of a segment in the diagram.

Based on the description provided, it seems like we are dealing with geometric statements about a diagram involving line segments and points labeled \(C\) and \(D\). Although I cannot view the actual diagram, I can walk you through how to assess each statement based on typical geometric reasoning.

1. **\( \overline{CD} \) is a perpendicular bisector.**  
   - For \( \overline{CD} \) to be a perpendicular bisector, it must both bisect another line segment (i.e., split it into two equal parts) and be perpendicular to it. Without seeing the diagram, I can't confirm this, but this would be true if \( \overline{CD} \) is intersecting another line perpendicularly at its midpoint.

2. **\( \overline{CD} \) is an angle bisector.**  
   - For this to be true, \( \overline{CD} \) must divide an angle into two congruent angles. This statement depends on whether \( \overline{CD} \) is shown bisecting an angle in the diagram.

3. **\(C\) is the vertex of a pair of congruent angles in the diagram.**  
   - This would be true if the diagram shows two angles with vertex \(C\) that have the same measure. This is often the case in isosceles triangles or when a line bisects an angle.

4. **\(C\) is the vertex of a right angle.**  
   - This would be true if one of the angles at \(C\) is a right angle (90°), which can be verified by the diagram if marked or inferred from perpendicular lines.

5. **\(C\) is the midpoint of a segment in the diagram.**  
   - For this to be true, \(C\) must lie on a line segment and divide it into two equal parts. This depends on how \(C\) is positioned in the diagram.

6. **\(D\) is the midpoint of a segment in the diagram.**  
   - Similar to the previous statement, \(D\) must lie on a line segment and divide it into two equal parts.

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Since I don't have the diagram, the truth of these statements hinges on how the points \(C\), \(D\), and the line segments are arranged. To confirm the answers, you would need to check the diagram to see how \( \overline{CD} \), the angles at \(C\), and the positioning of \(D\) align with the definitions of perpendicular bisectors, angle bisectors, congruent angles, right angles, and midpoints.

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Do you have any specific details from the diagram that might help clarify? I'd be happy to go over any part of this in more detail!

### 5 Related Questions:
1. What is the definition of a perpendicular bisector in geometry?
2. How do you determine if a line is an angle bisector?
3. What conditions must be met for angles to be congruent?
4. How can you identify the midpoint of a line segment?
5. What is the geometric significance of a right angle?

### Tip:
Always check for markings like equal-length segments, right-angle indicators, or bisectors in diagrams to confirm geometric relationships.

Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.) A B C D An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-N for Nemeth. Answer: CD is a perpendicular bisector. CD is an angle bisector. C is the vertex of a pair of congruent angles in the diagram. C is the vertex of a right angle. C is the midpoint of a segment in the diagram. D is the midpoint of a segment in the diagram.

Explore key geometric concepts such as perpendicular bisectors, angle bisectors, congruent angles, and midpoints in this detailed problem solution. Learn how these geometric properties apply to diagrams with points C and D, suitable for students in Grades 8-10.

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