Which of the following has no sets of parallel sides?
A Rectangle
B Rhombus
C Square Kite
D Parallelogram
E Isosceles Trapezoid
F Trapezoid
G Quadrilateral
The correct answer and explanation is:
The correct answer is Kite (C).
Explanation:
To understand which shape has no sets of parallel sides, let’s look at the properties of each option:
- Rectangle (A): A rectangle has two sets of parallel sides. Opposite sides are equal in length and parallel to each other.
- Rhombus (B): A rhombus also has two sets of parallel sides. All sides are of equal length, and opposite sides are parallel.
- Square (C): A square has all the properties of a rectangle and a rhombus. It has two sets of parallel sides, as opposite sides are parallel and equal in length.
- Kite (D): A kite has no sets of parallel sides. Its distinct feature is that it has two pairs of adjacent sides that are equal in length, but no opposite sides are parallel. This makes it unique compared to other quadrilaterals.
- Parallelogram (E): A parallelogram has two sets of parallel sides. Opposite sides are parallel and equal in length.
- Isosceles Trapezoid (F): An isosceles trapezoid has one set of parallel sides (the top and bottom). The non-parallel sides are of equal length, but they are not parallel to each other.
- Trapezoid (G): A trapezoid has exactly one set of parallel sides, which are its two opposite sides.
- Quadrilateral (H): A quadrilateral, in general, refers to any four-sided figure. It may or may not have parallel sides, depending on the type of quadrilateral. For instance, a general quadrilateral can have no parallel sides (e.g., an irregular quadrilateral).
Conclusion:
Among all the shapes listed, the Kite (D) is the only one that does not have any parallel sides. It has two pairs of adjacent sides of equal length, but none of the opposite sides are parallel to each other.