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:
An equilateral triangle has only 1 line of symmetry because it has 3 sides.
Corrected: An equilateral triangle has 3 lines of symmetry, one from each vertex to the midpoint of the opposite side.
Because all three sides of an equilateral triangle are equal, you can draw a fold line from each vertex to the middle of the opposite side, giving it 3 lines of symmetry, not 1.
2. Fix the sentence:
Intersecting lines must always form right angles.
Corrected: Intersecting lines cross at a point but do not always form right angles. Only perpendicular lines form right angles.
Intersecting lines cross at a point, but the angles they form can be any size. Only the special case called perpendicular lines always creates right angles (90 degrees).
3. Fix the sentence:
A line and a ray are the same thing because they both go on forever.
Corrected: A line goes on forever in both directions, but a ray has one endpoint and goes on forever in only one direction.
A line extends forever in both directions with no endpoints, while a ray has one endpoint and extends forever in only one direction. They are not the same thing.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. When two lines cross at one point, they are called intersecting lines.
When two lines meet or cross at exactly one point, mathematicians call them intersecting lines because "intersect" means to cross.
2. A regular hexagon has 3 pairs of parallel sides.
A regular hexagon has 6 sides, and each side is parallel to the side directly across from it, creating 3 separate pairs of parallel sides.
3. The letter W has 1 line(s) of symmetry.
The letter W has 1 line of symmetry running vertically down its center, because the left half mirrors the right half.
4. A point marks an exact location in space and has no size.
In geometry, a point shows an exact location but has no length, width, or height. It is usually drawn as a small dot and labeled with a capital letter.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Name two objects in a classroom that show perpendicular lines.
Sample answer: The edges where a wall meets the floor form perpendicular lines, and the corner of a book where two sides meet also shows perpendicular lines.
A good answer includes: The edges where a wall meets the floor form perpendicular lines, and the corner of a book where two sides meet also shows perpendicular lines.
2. Why does a scalene triangle have zero lines of symmetry?
Sample answer: A scalene triangle has all three sides of different lengths, so there is no line you can fold along to make both halves match exactly.
A good answer includes: A scalene triangle has all three sides of different lengths, so there is no line you can fold along to make both halves match exactly.