What Is a Quadrilateral?
Before we dive into specific shapes, let's make sure we understand the big family they all belong to.
A quadrilateral is any closed, flat (2D) shape that has exactly four straight sides and four angles. The word comes from Latin: quad = four, lateral = side.
Every quadrilateral has:
- 4 sides
- 4 vertices (corners)
- 4 interior angles that always add up to
Think of a quadrilateral as the "last name" for a big family of shapes. Squares, rectangles, and parallelograms are all members of the quadrilateral family — just like golden retrievers, poodles, and bulldogs are all members of the dog family.
In this topic, we'll explore three important quadrilaterals: the parallelogram, the rectangle, and the square. You'll learn what makes each one special and how they're related to each other.
The Parallelogram
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel and equal in length.
Here are the key properties of a parallelogram:
- Opposite sides are parallel: Side and side
- Opposite sides are equal in length: and
- Opposite angles are equal: and
- Consecutive angles are supplementary: This means any two angles next to each other add up to . For example,
- Diagonals bisect each other: The two diagonals cut each other exactly in half at their crossing point
Imagine a rectangle that has been gently pushed sideways so it "leans" — like a stack of books tilting on a shelf. The top and bottom stay parallel, the sides stay parallel, but the angles are no longer . That tilted shape is one example of a parallelogram! Keep in mind though, a parallelogram can lean a little or a lot — any angle is possible, as long as both pairs of opposite sides stay parallel.
The diagonals of a general parallelogram are not equal in length, they do not cross at right angles, and they do not bisect the corner angles. Those are special properties that only belong to specific types of parallelograms (like rectangles, rhombuses, and squares).
13 more sections in this topic
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