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Question

Lucy followed these steps. Step 1. She started with CD on her paper. She folded her paper so that point C was on top of point D. Step 2. She unfolded her paper and labeled the intersection of the fold and the line segment with point E. Step 4. She used a straight edge to draw QR at an arbitrary angle through point E. Step 5. Finally she drew CR through points C and R and DR through points D and R. What can you tell about CE and DE in this scenario.
Answers are: 1. the two segments are ray 2. The two segments are perpendicular. 3. The two segments are congruent. 4. The two segments are parallel.

Answer 1

In the scenario described, Lucy folds the paper so that point C lies directly on top of point D. When she unfolds the paper, point E is created as the intersection of the fold (the crease) and the line segment CD.

The crease formed by the fold would be the perpendicular bisector of line segment CD, meaning it intersects CD at its midpoint (point E) and forms right angles with the segment.

Thus, CE and DE are segments that share this midpoint E. Since E is the midpoint, the lengths of CE and DE are equal.

Based on this reasoning, the answer is: 3. The two segments are congruent.