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## Basics on the topicQuadrilaterals (Rhombus, Parallelogram, Trapezium)

Nico and Nia have snuck into a sweet factory, where they set off a machine. Sweets come down a conveyor belt in different shapes, and they need to sort these into the correct boxes to avoid trouble! They learn about the rhombus shape, parallelogram shape, and trapezium shape. This means they are able to avoid trouble because they now know the properties of a rhombus, the properties of a parallelogram, and the properties of a trapezium!

## What is a Parallelogram?

Parallelogram definition geometry: A parallelogram is a quadrilateral with two pairs of parallel sides.

### Parallelogram Properties

The properties of a parallelogram are:

• Opposite angles are equal
• Two pairs of parallel sides

The following illustration shows a parallelogram example with properties.

• What is a parallelogram shape? A parallelogram is a quadrilateral with opposite angles that are equal, and two pairs of parallel sides.
• How many sides does a parallelogram have? A parallelogram is a quadrilateral, which means it has four sides.
• Can parallelograms have right angles? A parallelogram CAN have right angles, as long as all the properties of a parallelogram are met.

## What is a Rhombus?

Rhombus definition geometry: A rhombus is a quadrilateral with all sides equal in length.

### Rhombus Properties

The properties of a rhombus are:

• Opposite angles are equal
• Four sides are ALL equal in length
• Two pairs of parallel sides

The following illustration shows a rhombus example with properties.

• How many sides does a rhombus have? A rhombus has four sides.
• What is the difference between a rhombus and a parallelogram? A rhombus is a parallelogram because it has two pairs of parallel sides. However, a rhombus must have four equal sides.
• Is a rhombus a quadrilateral? A rhombus is a quadrilateral because it has four sides.
• Does a rhombus have right angles? A rhombus CAN have right angles, but it doesn’t always need to have a right angle to be a rhombus.

## What is a Trapezium?

Trapezium definition geometry: A trapezium is a quadrilateral with one pair of parallel sides.

### Trapezium Properties

The properties of a trapezium are:

• One pair of parallel sides

The following illustration shows a trapezium example with properties.

• Can a trapezium be a parallelogram? A trapezium is not a parallelogram because it only has one pair of parallel sides, and a parallelogram must have two pairs of parallel sides.
• How many sides does a trapezium have? A trapezium has four sides but only one pair of parallel sides.

Nico and Nia are on a mission to sneak into a sweet factory. Luckily, they find an open window, so they climb inside. Nico spots a big button in the factory, but what is it for?

No Nico, you probably shouldn't. Oh look, now there's different shaped sweets coming out of the machine! Nico and Nia need to learn about Parallelograms, Rhombuses, and Trapeziums so they can sort the sweets into the correct boxes to avoid trouble!

"Quadrilaterals (Parallelogram, Rhombus, Trapezium)". A parallelogram, a rhombus, and a trapezium are all quadrilaterals. A "quadrilateral" is a "polygon with four straight sides." Parallelograms, Rhombuses, and Trapeziums are quadrilaterals that can be identified by their attributes, or properties. Let's learn about the properties of parallelograms before we help Nico and Nia. As you can see, a parallelogram can take many forms, like THESE shapes here. What is a property you notice parallelograms have?

All parallelograms have "Opposite angles" that are "EQUAL". THESE two angles are opposite and equal, and so are THESE two. Parallelograms also have "Two pairs of PARALLEL sides". PARALLEL lines never intersect, or cross each other. THESE two lines are parallel. And THESE two lines. "Parallelograms include rectangles and squares" to name some shapes that have two pairs of parallel sides. Now let's take a look at a Rhombus. What properties do we notice a Rhombus has?

Rhombuses have "Opposite angles" that are "EQUAL". THESE two angles are opposite and equal, and so are THESE two. Rhombuses also have "four sides ALL equal in length." THESE four sides are all equal in length. Finally, a rhombus also has "TWO pairs of parallel sides." THESE two lines are parallel. And the same HERE.

This means a rhombus can also be a parallelogram because it has TWO pairs of PARALLEL sides! Let's take a look at our last shape, a trapezium. What properties can you identify here?

Trapeziums have only "ONE pair of parallel sides". Can you find the parallel sides? THESE two lines are parallel because they do not cross or intersect! Trapeziums are NOT a type of parallelogram because THESE two sides will eventually intersect, or cross one another. A trapezium IS a type of quadrilateral, because it has FOUR sides. Now we can identify parallelograms, rhombuses, and trapeziums based on their properties, or attributes. Let's help Nico and Nia sort the three shapes of sweets before they cause a problem! First, we will start with THIS one. What properties do we notice?

It has opposite angles that are EQUAL and TWO pairs of parallel sides, but they are NOT all equal in length. Which box should it go in?

It needs to go in the PARALLELOGRAM box. Let's take a look at the second shape. What properties do you notice here?

It only has ONE pair of parallel sides because THESE two sides will eventually intersect. Based on the property we identified, which box should this sweet go in?

It needs to go in the TRAPEZIUM box because a trapezium has only ONE pair of parallel sides. Finally, we can sort the last shape. What properties do you notice?

It has opposite angles that are EQUAL. It also has four sides ALL EQUAL in length, plus two pairs of PARALLEL sides. Which box should this one go in?

It goes in the RHOMBUS box because a rhombus has opposite angles that are equal, and four equal sides that are parallel. Remember, Parallelograms, Rhombuses, and Trapeziums are quadrilaterals. PARALLELOGRAMS have opposite angles that are EQUAL and two pairs of PARALLEL sides. RHOMBUSES have opposite angles that are EQUAL and two pairs of PARALLEL sides. They also have four sides ALL equal in length. TRAPEZIUMS have only one pair of parallel sides. Phew, we helped Nico and Nia just in time! "Nia, don't put your hand too close to that machine!" Uh oh, too late. I wonder where Nia will end up?

Wait, what is Nico doing? "You're definitely not the right shape for this, Nia!"

## Quadrilaterals (Rhombus, Parallelogram, Trapezium) exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Quadrilaterals (Rhombus, Parallelogram, Trapezium).
• ### Correctly identify the quadrilaterals.

Hints

A rhombus has 4 sides of equal length.

A trapezium has only one set of parallel sides.

A parallelogram has 2 sets of parallel sides and opposite angles are equal.

Solution

Rhombus

4 equal length sides

2 sets of parallel sides

Opposite angles are equal

4 sided shape

Parallelogram

2 sets of parallel sides

Opposite angles are equal

4 sided shape

Trapezium

1 set of parallel sides

4 sided shape

Kite

No parallel sides

4 sided shape

2 equal length short sides and 2 equal length long sides

• ### Highlight the correct quadrilaterals.

Hints

Remember that a trapezium has only one pair of parallel sides.

Try rotating the shape to help you identify the features. This is a trapezium. It has one set of parallel sides.

Remember that a trapezium has only one pair of parallel sides. This shape has 2 sets of parallel sides so is NOT a trapezium.

Solution

There are 3 trapeziums in the picture.

• ### Properties of shapes.

Hints

Intersect means that the sides would eventually meet if they kept on going.

Look at these images of the trapeziums. What do you notice about the angles?

A parallelogram, a trapezium and a rhombus are all types of quadrilaterals. This means they must have 4 sides and 4 angles.

Solution

1. All parallelograms have 4 angles. True.

A parallelogram is a quadrilateral and all quadrilaterals have 4 sides and 4 angles.

2. A trapezium can have two right angles. True.

Some trapeziums have no right angles, however, a trapezium can have 2 right angles.

3. A triangle is a type of parallelogram. False.

A triangle is not a parallelogram because it has 3 sides, so can not be a quadrilateral.

4. A rhombus has sides that will eventually intersect. False.

A rhombus has 2 pairs of parallel sides. A pair of parallel sides will never intersect - they continue with a distance between them.

• ### Which shape is the odd one out?

Hints

All of these images have quadrilaterals in them. Three of them are the same and one is different.

A parallelogram has 2 pairs of parallel sides.

A trapezium has only 1 pair of parallel sides.

Solution

The odd one out is the rubber because this is a parallelogram.

All of the other shapes are trapeziums.

_____________________________________________________

We know this because a parallelogram has 2 pairs of parallel sides.

A trapezium has only 1 pair of parallel sides.

• ### Match the shapes.

Hints

The trapezium shaped sweets only have one pair of parallel sides.

The rhombus shaped sweets have 4 sides of equal length.

The rectangular sweets have two pairs of parallel sides and 4 right angles.

The square sweets have 4 right angles.

Solution

To find the matching sweet shapes, remember to think about the properties of each shape.

When the shapes are turned in different orientations, it can make them look different. Try to visualise rotating the shapes so that they are in another orientation to help you compare them.

• ### Name the shape.

Hints

A shape can be classified in more than one way. For example, a square can also be classed as something else.

A trapezium has only 1 set of parallel sides and 4 sides in total.

A parallelogram must have 2 pairs of parallel sides and only 4 sides in total.

Parallelograms and trapeziums are both types of quadrilaterals, that means they must have 4 sides.

Solution

A parallelogram is a 4 sided shape with 2 pairs of parallel sides. A square, a rectangle and a rhombus are all types of parallelogram.

A trapezium is a 4 sided shape with one pair of parallel sides. A trapezium can have 0 or 2 right angles.

Not a parallelogram or a trapezium.

A kite does not have any parallel sides.

A triangle is not a quadrilateral and therefore cannot be a parallelogram or a trapezium.

A cube is a 3D shape. Whilst its faces are square (parallelograms), the cube itself is not as it is not a 2D shape.