What Is a Quadrilateral?
Before we dive into specific shapes, let's make sure we're clear on the big idea.
A quadrilateral is any polygon with exactly four sides, four vertices (corners), and four interior angles that sum to .
You see quadrilaterals everywhere — book covers, phone screens, kite shapes in the sky, and tiles on a floor. In this subtopic we focus on three special quadrilaterals: the parallelogram, the trapezium, and the kite. Each one has its own unique combination of side lengths, parallel sides, angle relationships, and diagonal properties.
Whenever you need to identify or classify a quadrilateral, start by checking: (1) Are any sides parallel? (2) Are any sides equal in length? (3) What do the diagonals do? These three checks will guide you to the correct name every time.
The Parallelogram
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel and equal in length.
Key properties of a parallelogram:
- Opposite sides are parallel: and .
- Opposite sides are equal in length: and .
- Opposite angles are equal: and .
- Consecutive (adjacent) angles are supplementary — they add up to : .
- The diagonals bisect each other (they cut each other exactly in half), but they are not necessarily equal in length.
Imagine pushing a rectangle sideways so it leans over — you get a parallelogram. The opposite sides stay the same length and stay parallel, but the angles are no longer . A rectangle is actually a special case of a parallelogram where all angles happen to be right angles.
Because the diagonals bisect each other, if diagonal and diagonal meet at point , then and . This is a very useful property for solving problems involving missing lengths.
11 more sections in this topic
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