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← Back to Geometry
1Lines, Rays, Segments2Types of Angles3Triangles by Sides4Triangles by Angles5Quadrilaterals63D Solids7Parts of a Circle8Line Symmetry9Rotational Symmetry

Concept 5 of 9

Quadrilaterals

1

Today's big idea

Four angles always sum to 360°, and the most exact name is the one to give.

Every square is also a rectangle, a rhombus and a parallelogram.

2

How it works

👀 What's going on?

Four sides, four corners, and suddenly there are six names to keep straight. The names are not a random list. Each one is an earlier shape with one extra rule added.

💡 Here's the trick

Six quadrilaterals · sum = 360°SquareRectangleRhombusParallelogramTrapeziumKiteSquare ⊂ Rectangle · Square ⊂ Rhombus · all ⊂ Parallelogram

Look at the diagram above. The four angles of any four-sided shape add to 360°. A trapezium has exactly one pair of parallel sides. A parallelogram has two such pairs. A rhombus is a parallelogram with four equal sides, and a rectangle is one with four square corners. A square has both, so it counts as a rectangle and a rhombus as well. A kite is the odd one out, with two pairs of equal sides that sit side by side.

🪄 How to do it

  1. 1.Count the pairs of parallel sides in the diagram above.
  2. 2.Check which sides are equal and how many corners are square.
  3. 3.Give the shape the most exact name those clues allow.

✍️ Try it

One shape has a single pair of parallel sides and no others. What is its most exact name? Then: another shape has opposite sides equal and parallel, four square corners, and sides of two different lengths. What is its most exact name?

One pair of parallel sides and no more makes it a trapezium. Opposite sides parallel, four square corners and unequal side lengths make it a rectangle.

⚠️ Watch out

You might be thinking that a square cannot also be called a rectangle. A rectangle needs opposite sides equal and four square corners, and a square has both. So every square is a rectangle, a rhombus and a parallelogram, though square is still its most exact name.

🌟 Why this matters

Floor tiles, window frames, kite fabric and road signs are each cut to one of these shapes. A carpenter who orders a rhombus when a square was wanted wastes the whole sheet. The right name carries the right set of rules along with it.
Exam tip: When a question asks you to name a shape, always give the most exact name that fits.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“A quadrilateral has exactly ONE pair of parallel sides. What is it?”

  1. 1

    Count the parallel pairs

    Only one pair of sides is parallel. ▱

  2. 2

    Rule out the parallelogram

    A parallelogram needs two parallel pairs.

  3. 3

    Match the name

    One parallel pair only → trapezium.

  4. 4

    Answer ✓

    It is a trapezium.

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

2 pairs of parallel sides = parallelogram. 1 pair = trapezium. 2 pairs of adjacent equal sides = kite.

QUADRILATERAL SORT · ROUND 1 OF 2 · SORT ALL 6

5

Quick check

✅ VERIFICATION

Three angles of a quadrilateral are 90°, 85° and 100°. What is the fourth angle?

⚡ Finish the activity above first to answer.

Keep going!

Up next: 3D Solids

Euler: F + V − E = 2.

Concept 6 of 9 →