Properties of Quadrilaterals worksheet for geometry learning.

Let's solve this step-by-step based on the image you've provided. The task is to match each shape (labeled A–H) with its correct name and properties from the list of quadrilaterals and their characteristics.

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🔷 Step 1: Understand the Shapes

We have eight shapes labeled A to H, and we need to match them to one of the following quadrilateral types:

- Rectangle
- Arrowhead
- Rhombus
- Trapezium
- Square
- Kite
- Parallelogram

Also, there are descriptions in the right column that define each shape by properties.

Let’s go through each shape and match it to the correct name and properties.

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🔷 Step 2: Analyze Each Shape

#### Shape A
- Looks like a rectangle (four right angles, opposite sides equal and parallel).
- Matches: Rectangle
- Properties:
- Opposite sides equal
- Opposite sides parallel
- 4 right angles
- Diagonals cross at right angles? → Wait, diagonals in a rectangle do NOT necessarily cross at right angles unless it's a square.
- But let's check other options.

Wait — let's look carefully at the properties listed on the right.

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🔷 Step 3: Match Descriptions to Names

Let’s analyze the descriptions on the right and assign names to them first.

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#### ✔ Description 1:
> Name:
> Opposite sides equal
> Opposite sides parallel
> 4 right angles

→ This is a Rectangle

But note: Diagonals cross at right angles is not true for all rectangles. Only squares have diagonals that cross at right angles.

So if a shape has "diagonals cross at right angles", it must be a square or a rhombus.

Let’s look at the descriptions carefully.

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🔷 List of Descriptions and Their Matching Shapes

Let’s go through the descriptions one by one.

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#### 🟦 Description 1:
> Name:
> Opposite sides equal
> Opposite sides parallel
> 4 right angles

→ This is Rectangle

→ Which shape matches this?

- Shape A: Looks like a rectangle (longer than wide), no right angles marked, but assumed.
- Shape C: Square (all sides equal, right angles)

But wait — C has all sides equal and right angles → so it's a square, which is a special rectangle.

But description says “Opposite sides equal” — that applies to both rectangle and square.

But only one shape can be assigned per property set.

So let’s look at the next ones.

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#### 🟨 Description 2:
> Name:
> 2 pairs of equal sides
> 1 line of symmetry

→ This is a Kite

Because a kite has two pairs of adjacent equal sides and usually one line of symmetry.

Look at Shape B — it looks like a kite (diamond-like with a point at top). Yes.

✔ So B = Kite

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#### 🟩 Description 3:
> Name:
> All sides equal
> Opposite sides parallel
> Diagonals cross at right angles
> No right angles

→ This is a Rhombus

- All sides equal → rhombus or square
- Opposite sides parallel → yes
- Diagonals cross at right angles → yes (in rhombus)
- No right angles → so not a square

So this is Rhombus

Which shape matches this?

Look at Shape D — it's a parallelogram with slanted sides, but not a rectangle.

Wait — Shape D looks like a parallelogram, but not a rhombus unless all sides are equal.

But in the diagram, D appears to have all sides equal? Let’s see.

Actually, looking closely:

- Shape G is a diamond shape (like a rhombus), but not a square.
- Shape H is a kite or arrowhead?

Wait — let’s label each shape:

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🔷 Labeling the Shapes

Let’s go down from top to bottom:

- F: Trapezium (one pair of parallel sides) — looks like a trapezoid
- D: Parallelogram (opposite sides parallel, not right angles)
- C: Square (all sides equal, right angles)
- B: Kite (pointed top, symmetric)
- A: Rectangle (long, right angles)
- G: Rhombus (diamond shape, all sides equal, no right angles)
- H: Arrowhead (a kite with one angle reflex — concave)

Wait — Arrowhead is a type of kite but concave.

So let’s re-analyze.

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🔷 Now Match Shapes to Descriptions

Let’s go through the descriptions and find the matching shape.

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#### 🔹 Description 1:
> Opposite sides equal
> Opposite sides parallel
> 4 right angles

→ This is Rectangle

→ Matches Shape A (looks like a rectangle)

✔ A = Rectangle

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#### 🔹 Description 2:
> 2 pairs of equal sides
> 1 line of symmetry

→ This is Kite

→ Shape B is a kite (symmetric, two pairs of adjacent equal sides)

✔ B = Kite

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#### 🔹 Description 3:
> All sides equal
> Opposite sides parallel
> Diagonals cross at right angles
> No right angles

→ This is Rhombus

→ Shape G is a diamond-shaped figure, all sides appear equal, no right angles.

✔ G = Rhombus

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#### 🔹 Description 4:
> All sides equal
> Opposite sides parallel
> 4 right angles
> Diagonals cross at right angles

→ This is Square

→ Shape C is a square (equal sides, right angles)

✔ C = Square

Note: Square satisfies all these, including diagonals crossing at right angles.

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#### 🔹 Description 5:
> 2 pairs of equal adjacent sides
> Diagonals cross at right angles

→ This is Kite

Wait — but Description 2 already said "2 pairs of equal sides" → that’s also kite.

But here it says adjacent sides → same thing.

But wait — Description 5 says:

> 2 pairs of equal adjacent sides
> Diagonals cross at right angles

This is also a kite — but we already used kite for B.

Wait — but Shape H is an arrowhead, which is a concave kite.

But both kites and arrowheads can have two pairs of adjacent equal sides and diagonals crossing at right angles.

But let’s see:

- Description 5 says: 2 pairs of equal adjacent sides, diagonals cross at right angles → Kite

But we already have B as kite.

Wait — maybe two different kites?

But only one "kite" name.

Wait — perhaps Description 5 is for H?

But H is labeled as Arrowhead.

Ah! Here's the key:

The top row lists:

- Rectangle, Arrowhead, Rhombus, Trapezium
- Square, Kite, Parallelogram

So Arrowhead is a separate category — it's a concave kite.

So let’s check:

#### 🔹 Description 6:
> 1 pair of parallel lines

→ This is Trapezium

→ Shape F has one pair of parallel sides (top and bottom)

✔ F = Trapezium

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#### 🔹 Description 7:
> Opposite sides are equal
> 2 pairs of parallel sides
> No right angles

→ This is Parallelogram

→ Shape D has opposite sides equal and parallel, no right angles

✔ D = Parallelogram

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Now we have:

- A: Rectangle → matches Description 1
- B: Kite → matches Description 2
- C: Square → matches Description 4
- D: Parallelogram → matches Description 7
- F: Trapezium → matches Description 6
- G: Rhombus → matches Description 3
- H: Arrowhead → matches ???

Wait — we’re missing one description.

Let’s list all descriptions again:

There are 7 descriptions, but 8 shapes.

Wait — no, look:

Shapes: A, B, C, D, F, G, H — that’s 7 shapes.

Wait — labels: F, D, C, B, A, G, H → 7 shapes.

Yes, 7 shapes.

Now, descriptions:

1. Opposite sides equal, opposite sides parallel, 4 right angles → Rectangle → A
2. 2 pairs of equal sides, 1 line of symmetry → Kite → B
3. All sides equal, opposite sides parallel, diagonals cross at right angles, no right angles → Rhombus → G
4. All sides equal, opposite sides parallel, 4 right angles, diagonals cross at right angles → Square → C
5. 2 pairs of equal adjacent sides, diagonals cross at right angles → ???
6. 1 pair of parallel lines → Trapezium → F
7. Opposite sides equal, 2 pairs of parallel sides, no right angles → Parallelogram → D

Wait — now we have 7 descriptions, but description 5 is still unassigned.

But we’ve assigned:

- A → Desc 1
- B → Desc 2
- C → Desc 4
- D → Desc 7
- F → Desc 6
- G → Desc 3
- H → ???

Only H left.

And description 5 is:

> Name:
> 2 pairs of equal adjacent sides
> Diagonals cross at right angles

→ This is a Kite or Arrowhead?

But H is an arrowhead — a concave kite.

And arrowheads have:

- Two pairs of adjacent equal sides
- One diagonal is axis of symmetry
- Diagonals cross at right angles (usually)
- One reflex angle

So yes — arrowhead fits this description.

But the name should be Arrowhead

So:

✔ H = Arrowhead

And the description for H is:

> 2 pairs of equal adjacent sides
> Diagonals cross at right angles

So description 5 is for H.

But wait — description 2 was also for kite.

But B is a convex kite, H is a concave kite (arrowhead).

So both are types of kites, but arrowhead is specifically a concave kite.

In many curricula, arrowhead is treated separately.

So the descriptions are:

- B: Kite (convex)
- H: Arrowhead (concave)

But both share similar properties.

So likely:

- Description 2: 2 pairs of equal sides, 1 line of symmetry → Kite (B)
- Description 5: 2 pairs of equal adjacent sides, diagonals cross at right angles → Arrowhead (H)

But wait — description 5 says "2 pairs of equal adjacent sides" — same as kite.

And "diagonals cross at right angles" — true for both.

But description 2 has "1 line of symmetry" — which H also has.

So why two descriptions?

Wait — let’s check the exact wording.

Looking back:

> Description 2:
> Name:
> 2 pairs of equal sides
> 1 line of symmetry

→ This could be kite or arrowhead

> Description 5:
> Name:
> 2 pairs of equal adjacent sides
> Diagonals cross at right angles

→ Also kite/arrowhead

But B is convex kite → has one line of symmetry → matches desc 2

H is arrowhead → also has one line of symmetry → so both match?

But only one can be assigned.

Wait — perhaps description 5 is meant for B, and description 2 is for H?

No — they are separate.

Wait — maybe description 5 is actually for G?

No — G is rhombus, which has all sides equal, not just two pairs.

Let’s try to assign based on the shapes.

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🔷 Final Matching

Let’s go shape by shape:

| Shape | Visual | Likely Name | Reason |
|-------|--------|-------------|--------|
| A | Rectangle (long) | Rectangle | Opposite sides equal, parallel, 4 right angles |
| B | Kite (convex) | Kite | 2 pairs of equal adjacent sides, 1 line of symmetry |
| C | Square | Square | All sides equal, 4 right angles, diagonals cross at right angles |
| D | Slanted parallelogram | Parallelogram | Opposite sides equal and parallel, no right angles |
| F | Trapezium | Trapezium | One pair of parallel sides |
| G | Diamond (rhombus) | Rhombus | All sides equal, opposite sides parallel, diagonals cross at right angles, no right angles |
| H | Arrowhead (concave) | Arrowhead | 2 pairs of equal adjacent sides, diagonals cross at right angles |

Now, match to descriptions:

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🔷 Assigning Descriptions to Shapes

Let’s now assign the names and properties to each shape.

#### A → Rectangle
> Opposite sides equal
> Opposite sides parallel
> 4 right angles

✔ Matches Description 1

#### B → Kite
> 2 pairs of equal sides
> 1 line of symmetry

✔ Matches Description 2

#### C → Square
> All sides equal
> Opposite sides parallel
> 4 right angles
> Diagonals cross at right angles

✔ Matches Description 4

#### D → Parallelogram
> Opposite sides equal
> 2 pairs of parallel sides
> No right angles

✔ Matches Description 7

#### F → Trapezium
> 1 pair of parallel lines

✔ Matches Description 6

#### G → Rhombus
> All sides equal
> Opposite sides parallel
> Diagonals cross at right angles
> No right angles

✔ Matches Description 3

#### H → Arrowhead
> 2 pairs of equal adjacent sides
> Diagonals cross at right angles

✔ Matches Description 5

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✔ Final Answer:

Now, fill in the blanks:

| Shape | Name | Properties |
|-------|--------------|-----------|
| F | Trapezium | 1 pair of parallel lines |
| D | Parallelogram| Opposite sides equal, 2 pairs of parallel sides, no right angles |
| C | Square | All sides equal, opposite sides parallel, 4 right angles, diagonals cross at right angles |
| B | Kite | 2 pairs of equal sides, 1 line of symmetry |
| A | Rectangle | Opposite sides equal, opposite sides parallel, 4 right angles |
| G | Rhombus | All sides equal, opposite sides parallel, diagonals cross at right angles, no right angles |
| H | Arrowhead | 2 pairs of equal adjacent sides, diagonals cross at right angles |

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📌 Summary:

- A → Rectangle
- B → Kite
- C → Square
- D → Parallelogram
- F → Trapezium
- G → Rhombus
- H → Arrowhead

Each matches the corresponding description.

✔ All matched correctly.

Let me know if you'd like a printed version or a table format!