Classify quadrilaterals
Quadrilaterals are a family of four-sided shapes. Think of it like a family tree: they all share some traits, but each has its own special properties. Let's explore the relationships between them! 👨👩👧👦
Do this: Read the concept below, then try the quiz or activity.
Concept
In fifth grade, we classify quadrilaterals based on a hierarchy. This means some shapes are special types of other shapes.
The Quadrilateral Family Tree
1. Quadrilateral: The head of the family. The only rule is that it must have four sides.
2. Trapezoid: This is a quadrilateral with at least one pair of parallel sides.
3. Parallelogram: This is a more specific type of trapezoid. It has two pairs of parallel sides.
* *Property:* Opposite sides are equal in length.
* *Property:* Opposite angles are equal.4. Rhombus: A special parallelogram where all four sides are equal in length.
* Think of a tilted square.5. Rectangle: A special parallelogram where all four angles are right angles (90°).
* Think of a stretched-out square.6. Square: The most specific shape! A square is a parallelogram, a rhombus, AND a rectangle.
* It has two pairs of parallel sides.
* All four sides are equal (like a rhombus).
* All four angles are right angles (like a rectangle).Thinking Hierarchically This means you can call a shape by more than one name! * A square can also be called a rectangle, a rhombus, a parallelogram, a trapezoid, and a quadrilateral. It fits all the rules! * A rectangle can also be called a parallelogram, a trapezoid, and a quadrilateral (but it's not always a rhombus or a square). * A rhombus can also be called a parallelogram, a trapezoid, and a quadrilateral (but it's not always a rectangle or a square).
Key Idea: To classify a shape, check its properties (parallel sides, side lengths, angles) and see which categories it fits into, from most general (quadrilateral) to most specific (square).
Try it
Practice classifying quadrilaterals!
True or False? 1. All squares are rectangles. 2. All rectangles are squares. 3. All rhombuses are parallelograms. 4. All trapezoids are parallelograms. 5. A square is a rhombus.
Check all the names that apply for each shape: 6. A square: (Quadrilateral, Trapezoid, Parallelogram, Rectangle, Rhombus, Square) 7. A rectangle that is not a square: (Quadrilateral, Trapezoid, Parallelogram, Rectangle, Rhombus, Square) 8. A rhombus that is not a square: (Quadrilateral, Trapezoid, Parallelogram, Rectangle, Rhombus, Square)
Answer the question: 9. What is the difference between a parallelogram and a trapezoid? 10. What property does a rectangle have that a rhombus does not always have? 11. What property makes a square a special kind of rectangle?
Challenge Problems: 12. Draw a quadrilateral that is not a trapezoid. (Hint: no parallel sides). 13. Can you draw a rhombus that is also a rectangle? What shape is it?