A quadrilateral is a shape closed in by four straight sides.
You can find many kinds around you: a notebook, a window, a kite, the side of a staircase.
Depending on how many pairs of parallel sides they have and on their side lengths and angles, quadrilaterals are called trapezoids, parallelograms, rhombuses, rectangles and squares, and the more conditions a shape meets, the more special it is.
Choose a quadrilateral with the buttons to see its conditions marked on it; the picture below shows how the kinds fit inside one another.
Kinds of Quadrilaterals
🔷 Sorting by Parallel Sides and Lengths
①A quadrilateral with at least one pair of parallel sides is a trapezoid
②If both pairs of opposite sides are parallel, it is a parallelogram
③If all four sides are equal it is a rhombus, and if all four angles are right angles it is a rectangle
④A shape that is both a rhombus and a rectangle is a square
Comparing Quadrilaterals
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The chosen quadrilateral with its sides, angles, parallel sides and diagonals marked
How They Fit Together
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Trapezoids containing parallelograms, which contain rectangles and rhombuses, which contain squares
🪆 Quadrilaterals Fit Inside Each Other
①A parallelogram has parallel sides, so it is also a trapezoid
②Rectangles and rhombuses have parallel opposite sides, so they are parallelograms
③A square has four right angles and four equal sides, so it is both a rectangle and a rhombus
④It does not work the other way: not every trapezoid is a parallelogram
Summary
Square
All sides equal + all angles = 90°
Both a rectangle and a rhombus, the quadrilateral with the most conditions
Rectangle
All angles = 90°
Its opposite sides are also equal
Parallelogram
Both pairs of opposite sides parallel
Its opposite sides are equal, and so are its opposite angles
🎯 Summary
①Trapezoid: at least one pair of parallel sides
②Parallelogram: both pairs of opposite sides parallel
③Rhombus: four equal sides
④Rectangle: four right angles
⑤Square: four equal sides and four right angles, so it belongs to all four groups above
Examples and Unit Test
Example 1
What is a quadrilateral with four equal sides and four right angles called?
1
Four equal sides make it a rhombus, and four right angles make it a rectangle.
2
A shape that is both a rhombus and a rectangle is a square.
▸ Square
A square meets the conditions of a trapezoid, a parallelogram, a rhombus and a rectangle all at once.
Example 2
What is a quadrilateral with exactly one pair of parallel sides called?
1
Count the pairs of parallel sides.
2
It has a pair of parallel sides, so it is a trapezoid; both pairs would have to be parallel for a parallelogram.
▸ Trapezoid
Parallelograms count as trapezoids too, but a shape with only one pair of parallel sides is not a parallelogram.
Unit Test
Which is the best name for a quadrilateral with four right angles whose opposite sides are equal?
①rhombus
②rectangle
③trapezoid
④parallelogram
▸ ② rectangle
1
Look for the quadrilateral whose four angles are all right angles.
2
That is a rectangle. A rectangle is also a parallelogram, but rectangle is the name that describes it most exactly.