Classifying 2D Figures • Topic 1 of 2

Hierarchy of Quadrilaterals

What is a Quadrilateral?

A quadrilateral is a polygon with 4 sides and 4 angles.

Quadrilateral Family Tree:

                        QUADRILATERAL
                      (4 sides, 4 angles)
                             │
            ┌────────────────┼────────────────┐
            │                │                │
        TRAPEZOID        PARALLELOGRAM     (Other: kite, etc.)
      (1 pair of    (2 pairs of parallel
       parallel           sides)
         sides)              │
                ┌────────────┼────────────┐
                │            │            │
            RECTANGLE     RHOMBUS       SQUARE?
            (4 right   (4 equal sides,   (special case!)
             angles)    not right angles)
                │            │
                └──────┬─────┘
                       │
                    SQUARE
            (4 right angles + 4 equal sides)

Quadrilateral Hierarchy:

Shape	Properties
Trapezoid	1 pair of parallel sides
Parallelogram	2 pairs of parallel sides, opposite sides equal
Rectangle	Parallelogram + 4 right angles
Rhombus	Parallelogram + 4 equal sides
Square	Rectangle + Rhombus (4 right angles + 4 equal sides)

QUADRILATERAL HIERARCHY DIAGRAM:

 ┌─────────────────┐
 │ QUADRILATERAL │
 │ (4 sides) │
 └────────┬────────┘
 │
 ┌────────────────┼────────────────┐
 │ │ │
 ▼ ▼ ▼
 ┌───────────┐ ┌───────────┐ ┌───────────┐
 │ TRAPEZOID │ │PARALLELO- │ │ KITE │
 │1 pair ∥ │ │ GRAM │ │2 pairs │
 └───────────┘ │2 pairs ∥ │ │adj = sides│
 └─────┬─────┘ └───────────┘
 │
 ┌──────────────┼──────────────┐
 │ │ │
 ▼ ▼ ▼
 ┌───────────┐ ┌───────────┐ ┌───────────┐
 │ RECTANGLE │ │ RHOMBUS │ │ SQUARE? │
 │4 right ∠s │ │4 = sides │ │(needs both│
 └─────┬─────┘ └─────┬─────┘ │ properties│
 │ │ └───────────┘
 └────────┬───────┘
 │
 ▼
 ┌───────────┐
 │ SQUARE │
 │4 right ∠s │
 │4 = sides │
 └───────────┘


VISUAL EXAMPLES OF EACH:

 TRAPEZOID PARALLELOGRAM RECTANGLE
 /‾‾‾‾‾ /‾‾‾‾‾ ┌─────┐
 / / │ │
 / / │ │
 /___________ /___________ └─────┘
 
 RHOMBUS SQUARE
 ◇ ┌───┐
 / │ │
 / │ │
 /______ └───┘

Solved Examples

Worked Example

A shape has 2 pairs of parallel sides and 4 right angles. What is it?

Solution

2 pairs of parallel sides = parallelogram
4 right angles = rectangle
Could also be square if sides equal, but rectangle is correct
Answer: Rectangle

Worked Example

Draw the hierarchy from widest to narrowest: square, quadrilateral, rectangle, parallelogram

Solution

Widest: Quadrilateral
Then: Parallelogram
Then: Rectangle
Narrowest: Square
Answer: Quadrilateral → Parallelogram → Rectangle → Square

Worked Example

A trapezoid has how many pairs of parallel sides?

Solution

Definition of trapezoid: exactly 1 pair of parallel sides
Answer: 1 pair

Key Points

Quadrilateral = any 4-sided polygon
Trapezoid = 1 pair of parallel sides
Parallelogram = 2 pairs of parallel sides
Rectangle = parallelogram + 4 right angles
Rhombus = parallelogram + 4 equal sides
Square = rectangle + rhombus (all properties!)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.A quadrilateral has how many sides?

Explanation: Four.

Q2.A square is a special:

Explanation: Rectangle (all sides equal).

Q3.Is every rectangle a square?

Explanation: No.

Q4.A rhombus has:

Explanation: All sides equal.

Practice more MCQs → 📝 Assignment · 35 marks