Have you ever used a quadrilateral in a real-world object? Take a look at this dilemma.
Margie makes jewelry. She made this necklace to sell at a craft fair.
Can you identify the quadrilateral? In this Concept, you will learn how to accomplish this task.
What is a quadrilateral?
A quadrilateral is any four-sided figure.
In the word “quadrilateral”, we find the word “quad” which means four. This means that any four-sided figure is considered a quadrilateral. Now, there are different types of quadrilaterals that we are going to learn about in this lesson.
We can say that a quadrilateral is any four-sided figure. We could consider this an umbrella category meaning that there are different types of quadrilaterals that we can identify in a specific way even though they are still quadrilaterals too.
Let’s look at identify the types of quadrilaterals.
The first type of quadrilateral to learn about is called a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel and congruent.
Here is a picture of a parallelogram.
When you look at this picture, you can see that the opposite sides of the figure are parallel. They are also the same length-meaning congruent.
There are three main kinds of parallelograms.
Parallelograms can be plain old parallelograms like the one in the picture. They could also be a rectangle, square and rhombus.
A rectangle is a parallelogram with four right angles, where opposite sides are congruent and parallel. You have been looking at rectangles for a long time, but now you need to notice that there are specific properties that make a rectangle a rectangle.
A rhombus is a parallelogram with four congruent sides, but not necessarily four right angles. A rhombus can look like a square, but while a square is always a rhombus, a rhombus is not necessarily a square. A rhombus can only be a square if it has four right angles.
A square is a parallelogram too. The big difference between a square and a rectangle is that a square has four congruent sides. It also has four right angles though just like a rectangle.
There is one other type of quadrilateral. This quadrilateral is NOT a parallelogram. It is a special kind of quadrilateral. It is called a trapezoid. A trapezoid is a quadrilateral with one pair of opposite sides parallel.
Find the measure of the unknown angle in the quadrilateral below.
Our calculation was correct. We can always use this method when given three out of the four angles in a quadrilateral.
Often we can use what we know about the properties of quadrilaterals to find unknown measures without having to set up an equation. We can simply use reasoning to put the pieces together.
Identify each missing angle.
Now let's go back to the dilemma from the beginning of the Concept.
Look at the necklace that Margie made once again.
Now let’s examine this picture. We can look for the qualities that identify this quadrilateral. Notice that it has two parallel sides. The other two sides aren’t parallel or congruent. With one pair of parallel sides, this figure must be a trapezoid.
any four-sided figure.
a quadrilateral with one pair of parallel sides.
a quadrilateral with two pairs of opposite sides that are congruent and parallel.
a parallelogram with four congruent sides.
a parallelogram with opposites congruent and four right angles.
a parallelogram with four congruent sides and four right angles.
means exactly the same.
Here is one for you to try on your own.
Find the measures of the unknown angles in the quadrilateral below.
They do, so our answers are correct.
Khan Academy Overview of Quadrilaterals
Directions: Use what you have learned about quadrilaterals to figure out the missing angle measure of each quadrilateral based on three given angles.