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Quadrilaterals (Rhombus, Parallelogram, Trapezoid)

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Quadrilaterals (Rhombus, Parallelogram, Trapezoid)
CCSS.MATH.CONTENT.3.G.A.1

Basics on the topic Quadrilaterals (Rhombus, Parallelogram, Trapezoid)

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Quadrilaterals – Rhombus, Parallelogram, Trapezoid

Perhaps you have already heard about rectangles and squares as kinds of quadrilaterals? Well, there are actually many more shapes that you can learn about! For example, the following text contains everything you need to know about the characteristics of the rhombus, parallelogram and trapezoid. Those names sound kind of fancy, right? This is what the shapes of a rhombus, parallelogram and trapezoid look like:

Shapes of parallelogram, rhombus, trapezoid

What is a Parallelogram Shape?

Per its definition in geometry, a parallelogram is a quadrilateral with two pairs of parallel sides.

Properties of a Parallelogram

The properties of a parallelogram are the following:

  • Opposite angles are equal
  • Two pairs of parallel sides

The following illustration shows an example of a parallelogram with its properties highlighted:

Parallelogram properties

What is a Rhombus Shape?

According to its definition in geometry, a rhombus is a quadrilateral with all sides equal in length.

Properties of a Rhombus

The properties that make up a rhombus are:

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

On the following infographic you can see an example of a rhombus with its properties accentuated:

Rhombus properties

What is a Trapezoid Shape?

Per its geometric definition, a trapezoid is a quadrilateral with one pair of parallel sides.

Properties of a Trapezoid

The main attribute of a trapezoid is the following:

  • One pair of parallel sides

You can see this property on the following illustration depicting a trapezoid example:

Trapezoid properties

Rhombus, Parallelogram, Trapezoid – Overview

The following table summarizes the attributes of the different shapes at a glance:

Shape Properties
parallelogram opposite angles equal

two pairs of parallel sides
rhombus opposite angles equal

four sides all equal in length

two pairs of parallel sides
trapezoid one pair of parallel sides

Below you will find some common questions and answers about parallelograms, rhombuses and trapezoids.

Frequently Asked Questions on the Topic Quadrilaterals – Rhombus, Parallelogram, Trapezoid

What does a parallelogram look like?
How many sides does a parallelogram have?
Does a parallelogram have four right angles?
Is a rhombus a parallelogram?
Is a rhombus a quadrilateral?
Does a rhombus have right angles?
Is a trapezoid a parallelogram?

Transcript Quadrilaterals (Rhombus, Parallelogram, Trapezoid)

Nico and Nia are on a mission to sneak into a candy 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 candy coming out of the machine. Nico and Nia need to learn about parallelograms, rhombuses, and trapezoids so they can sort the candy into the correct boxes to avoid trouble. Quadrilaterals (Parallelogram, Rhombus, Trapezoid). A Parallelogram, Rhombus, and Trapezoid are all quadrilaterals. A quadrilateral is a polygon with four straight sides. Parallelograms, rhombuses, and trapezoids are quadrilaterals that can be identified by their attributes, or properties. Let's learn about the attributes of parallelograms before we help Nico and Nia. As you can see, a parallelogram can take many forms, like these shapes here. What is an attribute 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 attributes 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 trapezoid. What attributes can you identify here? Trapezoids 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. Trapezoids are not a type of parallelogram because these two sides will eventually intersect, or cross one another. A trapezoid is a type of quadrilateral, because it has four sides. Now we can identify parallelograms, rhombuses, and trapezoids based on their properties, or attributes. Let's help Nico and Nia sort the three candy shapes before they cause a problem. First, we will start with this one. What attributes 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 candy shape. What attributes do you notice here? It has only one pair of parallel sides because these two sides will eventually intersect. Based on the attribute we identified, which box should this candy go in? It needs to go in the trapezoid box, because a trapezoid has only one pair of parallel sides. Finally, we can sort the last shape. What attributes 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 trapezoids 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. Trapezoids 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, Trapezoid) exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Quadrilaterals (Rhombus, Parallelogram, Trapezoid).
  • Identify the quadrilaterals.

    Hints

    A rhombus has 4 sides of equal length.

    A trapezoid 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

    Trapezoid

    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 trapezoids.

    Hints

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

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

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

    Solution

    There are 3 trapezoids in the picture.

  • Properties of shapes.

    Hints

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

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

    A parallelogram, a trapezoid 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 trapezoid can have two right angles. True.

    Some trapezoids have no right angles, however, a trapezoid 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 it cannot 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 the same distance between them.

  • Which shape doesn't belong?

    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 trapezoid only has 1 pair of parallel sides.

    Solution

    The object that doesn't belong is the eraser because this is a parallelogram.

    All of the other shapes are trapezoids.

    _____________________________________________________

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

    A trapezoid only has 1 pair of parallel sides.

  • Match the shapes.

    Hints

    The trapezoid shaped candies only have one pair of parallel sides.

    The rhombus shaped candies have 4 sides of equal length.

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

    The square candies have 4 right angles.

    Solution

    To find the matching candy 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 visualize 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 trapezoid 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 trapezoids 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 parallelograms.

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

    Not a parallelogram or a trapezoid.

    A kite does not have any parallel sides.

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

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