What is a quadrilateral that has a line of symmetry but no rotational symmetry?
Would that be trapezoid?
Yes, you are correct! A trapezoid is a quadrilateral that has a line of symmetry but no rotational symmetry.
To determine this, first, let's quickly review what these two types of symmetry mean:
1. Line of Symmetry: A line of symmetry is a line that divides a shape into two equal halves that are mirror images of each other. If a quadrilateral has a line of symmetry, it means that you can fold the shape along that line so that both halves match perfectly.
2. Rotational Symmetry: A shape has rotational symmetry if it can be rotated by some angle less than 360 degrees and still appear the same. For example, a square has rotational symmetry because it can be rotated by 90 degrees and still look the same.
Now, coming back to the question, a trapezoid (also known as a trapezium) is a quadrilateral with exactly one pair of parallel sides. It looks like a slanted rectangle, with one pair of sides being parallel while the other pair is not.
If you draw the line of symmetry on a trapezoid, it would be a line that divides the shape into two equal halves. However, if you try to rotate the trapezoid by any angle less than 360 degrees, it will not align with its original position. Therefore, a trapezoid has a line of symmetry but no rotational symmetry.