How are a parallelogram and a trapezoid different? A A trapezoid has ony 1 pair of parallel sides, but a paralelogram has 2. C.B.A parallelogram has 4 right angles, but a trapezoid doesn’t need to have 4 right angles CA parallelogram has only 1 pair of parallel sides, but a trapezoid has 2 D A trapezoid has 4 night angles, but a parallelogram doesn’t need to have 4 night angles
The Correct Answer and Explanation is:
The correct answer is A: A trapezoid has only 1 pair of parallel sides, but a parallelogram has 2.
Explanation:
A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. This means the opposite sides are not only equal in length but also run in the same direction, ensuring that they will never meet. In addition to parallel sides, a parallelogram also has opposite angles that are equal and adjacent angles that are supplementary (add up to 180°).
Some key properties of a parallelogram:
- Two pairs of parallel sides.
- Opposite sides are equal.
- Opposite angles are equal.
- Diagonals bisect each other.
On the other hand, a trapezoid (or trapezium in some countries) is a quadrilateral that has exactly one pair of parallel sides. The other two sides are not parallel and may be of different lengths. This shape can be further categorized into isosceles trapezoids (where the non-parallel sides are equal in length) and scalene trapezoids (where the non-parallel sides are unequal).
Some key properties of a trapezoid:
- One pair of parallel sides.
- The other two sides are non-parallel.
- The angles on the same side of the parallel sides are supplementary (i.e., they add up to 180°).
Why the other options are incorrect:
- B: A parallelogram does not necessarily have 4 right angles. In fact, it can have any angle, but in the case of a rectangle (a specific type of parallelogram), the angles are 90°.
- C: This is incorrect because a parallelogram has two pairs of parallel sides, not just one.
- D: A parallelogram does not require 4 right angles, while a trapezoid does not have to have any right angles at all.
So, the key difference is that a parallelogram has two pairs of parallel sides, while a trapezoid has only one pair.
