Properties of Quadrilaterals - Mr-Mathematics.com - Free Printable

Let’s go step by step to fill in the table correctly. We’ll look at each shape and answer the four questions based on its properties.

We are classifying these quadrilaterals:
- Kite
- Parallelogram
- Rhombus
- Square
- Rectangle
- Trapezium

And we need to answer for each:
1. Diagonals always equal in length?
2. Diagonals intersect at 90°?
3. How many pairs of parallel sides?
4. How many pairs of opposite angles are equal?

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Step 1: Kite

- Diagonals equal? → No, not always. One is usually longer.
- Intersect at 90°? → Yes! That’s a key property of kites.
- Pairs of parallel sides? → Usually zero. (Unless it’s a special case like a rhombus, but generally no.)
- Opposite angles equal? → Only one pair of opposite angles are equal (the ones between unequal sides).

→ So: No, Yes, 0, 1

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Step 2: Parallelogram

- Diagonals equal? → Not necessarily. Only if it’s a rectangle or square.
- Intersect at 90°? → Only if it’s a rhombus or square. Generally, no.
- Pairs of parallel sides? → Two pairs — that’s what makes it a parallelogram!
- Opposite angles equal? → Yes, both pairs of opposite angles are equal.

→ So: No, No, 2, 2

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Step 3: Rhombus

- Diagonals equal? → No, unless it’s a square. In a rhombus, diagonals are different lengths but bisect each other at 90°.
- Intersect at 90°? → Yes! Always.
- Pairs of parallel sides? → Two pairs — it’s a type of parallelogram.
- Opposite angles equal? → Yes, both pairs.

→ So: No, Yes, 2, 2

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Step 4: Square

- Diagonals equal? → Yes! All squares have equal diagonals.
- Intersect at 90°? → Yes! They cross at right angles.
- Pairs of parallel sides? → Two pairs — it’s a parallelogram too.
- Opposite angles equal? → Yes, all angles are 90°, so definitely opposite ones are equal.

→ So: Yes, Yes, 2, 2

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Step 5: Rectangle

- Diagonals equal? → Yes! Always.
- Intersect at 90°? → No, they bisect each other but not at 90° unless it’s a square.
- Pairs of parallel sides? → Two pairs — it’s a parallelogram.
- Opposite angles equal? → Yes, all angles are 90°, so opposite ones are equal.

→ So: Yes, No, 2, 2

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Step 6: Trapezium (Note: In some countries, “trapezoid” means one pair of parallel sides; here we assume trapezium = exactly one pair)

- Diagonals equal? → Sometimes, but not always. For example, in an isosceles trapezium they are equal, but not in all. The question says “always”, so answer is No.
- Intersect at 90°? → Rarely. Not a defining property. So No.
- Pairs of parallel sides? → Exactly one pair.
- Opposite angles equal? → Not necessarily. Only in isosceles trapeziums are base angles equal, but opposite angles aren’t necessarily equal. So generally, No.

→ So: No, No, 1, 0

*(Note: Some definitions say trapezium has NO parallel sides — but in most school curricula, especially with this diagram showing a typical trapezoid shape, it means ONE pair. Also, the diagram shows a trapezium with one pair of parallel sides.)*

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Now let’s put it all together in the table:

| Shape | Diagonals always equal in length? | Diagonals intersect at 90°? | How many pairs of parallel sides? | How many pairs of opposite angles are equal? |
|--------------|-----------------------------------|-----------------------------|----------------------------------|---------------------------------------------|
| Kite | No | Yes | 0 | 1 |
| Parallelogram| No | No | 2 | 2 |
| Rhombus | No | Yes | 2 | 2 |
| Square | Yes | Yes | 2 | 2 |
| Rectangle | Yes | No | 2 | 2 |
| Trapezium | No | No | 1 | 0 |

Final Answer:
Kite: No, Yes, 0, 1
Parallelogram: No, No, 2, 2
Rhombus: No, Yes, 2, 2
Square: Yes, Yes, 2, 2
Rectangle: Yes, No, 2, 2
Trapezium: No, No, 1, 0