Number line with points A, B, C, and D, demonstrating congruent line segments AB and CD.

Problem Analysis and Solution

The provided image contains a quiz worksheet on congruent segments. Let's solve each question step by step.

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#### Question 1:
> Mary bought two pencils that are completely equal in length. What are these pencils an example of?
>
> - Two congruent rays.
> - Two congruent line segments.
> - Two congruent lines.
> - Two congruent radii.

Solution:
- Congruent segments are segments that have the same length.
- Pencils, when considered as straight objects with finite lengths, can be thought of as line segments.
- Rays extend infinitely in one direction, so they cannot be "equal in length."
- Lines extend infinitely in both directions, so they also cannot be "equal in length."
- Radii are specific to circles and refer to the distance from the center to the circumference; this is not relevant here.

Thus, the correct answer is:
- Two congruent line segments.

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#### Question 2:
> What can you conclude from this image?
>
> \(\overline{AB} \cong \overline{CD}\)
>
> - Line AB is not congruent to CD.
> - Line segment AB is not congruent to CD.
> - Line AB is congruent to CD.
> - Line segment AB is congruent to line segment CD.

Solution:
- The notation \(\overline{AB} \cong \overline{CD}\) explicitly states that the line segment \(\overline{AB}\) is congruent to the line segment \(\overline{CD}\).
- This means they have the same length.
- The term "line" refers to an infinite object, while "line segment" refers to a finite portion of a line. Since the problem uses the notation \(\overline{AB}\) and \(\overline{CD}\), it is referring to line segments, not lines.

Thus, the correct answer is:
- Line segment AB is congruent to line segment CD.

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#### Question 3:
> In this image (if all spaces between numbers are equal) are line segments AB and CD congruent?
>
> [Number Line Image]
>
> - Yes
> - No
> - Partially
> - Not enough information

Solution:
- The number line shows points \(A\), \(B\), \(C\), and \(D\) marked at specific positions.
- To determine if \(\overline{AB}\) and \(\overline{CD}\) are congruent, we need to calculate their lengths.
- From the number line:
- Point \(A\) is at \(-6\).
- Point \(B\) is at \(-3\).
- Point \(C\) is at \(3\).
- Point \(D\) is at \(5\).
- Length of \(\overline{AB}\):
\[
\text{Length of } \overline{AB} = |B - A| = |-3 - (-6)| = |-3 + 6| = |3| = 3
\]
- Length of \(\overline{CD}\):
\[
\text{Length of } \overline{CD} = |D - C| = |5 - 3| = |2| = 2
\]
- Since the length of \(\overline{AB}\) is \(3\) and the length of \(\overline{CD}\) is \(2\), the two segments are not congruent.

Thus, the correct answer is:
- No

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Final Answers:

1. Two congruent line segments.
2. Line segment AB is congruent to line segment CD.
3. No

\[
\boxed{\text{Two congruent line segments, Line segment AB is congruent to line segment CD, No}}
\]