Lines and Symmetry — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A line segment goes on forever in one direction from its endpoint.
Corrected: A line segment has two endpoints and does not go on forever. A ray goes on forever in one direction from its endpoint.
A line segment has two endpoints and a fixed length, so it cannot go on forever. The original sentence described a ray, which starts at one endpoint and extends forever in one direction.
2. Fix the sentence:
The letter M has 3 lines of symmetry.
Corrected: The letter M has 1 line of symmetry, running vertically down the middle.
The letter M can only be folded along a vertical line down its center to create matching halves, so it has just 1 line of symmetry, not 3.
3. Fix the sentence:
Parallel lines always meet at a point far away.
Corrected: Parallel lines never meet no matter how far they extend.
Parallel lines stay the same distance apart and never cross, no matter how far you extend them. The original sentence confused parallel lines with lines that intersect.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The letter D has 1 line(s) of symmetry.
The letter D has 1 line of symmetry because you can fold it horizontally through the middle and the top and bottom halves match.
2. A ray is named by its endpoint and one other point on the ray.
A ray starts at its endpoint and goes on forever in one direction, so you name it by listing the endpoint first and then any other point along the ray.
3. Two lines that are not parallel and do not intersect in a flat surface are called skew lines.
Skew lines exist in different planes, so they never cross and are not parallel either. Think of a line on the floor and a line on the ceiling going a different direction.
4. The letter O has 2 lines of symmetry.
The letter O has 2 lines of symmetry because you can fold it vertically or horizontally through its center and both halves match each time.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How is a line segment different from a line?
Sample answer: A line segment has two endpoints and a fixed length, while a line extends forever in both directions with no endpoints.
A good answer includes: A line segment has two endpoints and a fixed length, while a line extends forever in both directions with no endpoints.
2. Name a capital letter that has no lines of symmetry and explain why.
Sample answer: The letter F has no lines of symmetry because you cannot fold it along any line and have both halves match exactly.
A good answer includes: The letter F has no lines of symmetry because you cannot fold it along any line and have both halves match exactly.