Download 1 Quadrilateral Classification

Quadrilateral Classification
Jen Kershaw
Kimberly Hopkins
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Printed: May 12, 2016
AUTHORS
Jen Kershaw
Kimberly Hopkins
www.ck12.org
C HAPTER
Chapter 1. Quadrilateral Classification
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Quadrilateral Classification
In this concept, you will learn how to identify and classify quadrilaterals.
Let’s Think About It
Rasha is helping her father paint the door frame of their home. She calls out the names of each shape that she paints.
She reaches a shape that she cannot name. She sees that it has four sides and one set of parallel sides. What shape is
she painting?
In this concept, you will learn how to identify and classify quadrilaterals.
Guidance
Polygons are closed shapes with sides made up of lines. Any closed shape with straight edges, such as a triangle or
rectangle, is a polygon.
Polygons with four sides, such as rectangles and squares, are called quadrilaterals. The prefix of this word “quad”
means four, therefore, a quadrilateral is a polygon that has four sides. Quadrilaterals also have four angles, and these
four angles have a sum of 360◦ . This is true for all quadrilaterals
Another important feature of quadrilaterals is that many have one or even two pairs of parallel sides. Look at the
quadrilaterals below.
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Let’s look at the different types of quadrilaterals in detail.
A parallelogram is a quadrilateral with opposite sides parallel. The first figure above is a parallelogram. There are
a few special features of parallelograms. One is that each pair of parallel sides is congruent. In the first figure above,
the two short sides are the same length and the two long sides are the same length. This special relationship between
the pairs of sides affects the angles of a parallelogram: the angles opposite each other are congruent. The 70◦ angles
are opposite each other, and the 110◦ angles are opposite each other. This relationship exists in any parallelogram,
no matter the length of the sides or the sizes of the angle pairs.
There are three special kinds of parallelograms.
A rectangle is a quadrilateral because it has four sides, and it is a parallelogram because it has two pairs of parallel,
congruent sides. All four angles are right angles.
A square has two pairs of parallel sides and four right angles. All four of its sides are congruent.
The third special parallelogram is called a rhombus. Like a square, a rhombus has four congruent sides and pairs of
congruent angles opposite each other. However, right angles are not required for a rhombus. So a rhombus canbe a
square, but a square isn’t necessarily a rhombus because of the right angles necessary in a square.
Let’s look at an example.
Identify the shape below as a rectangle, square, rhombus, or just a parallelogram.
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Chapter 1. Quadrilateral Classification
First, check the lengths of the sides.
The shape has four sides of equal lengths.
Next, check to see if the shape has four right angles.
The shape does not have four right angles.
Then, identify the shape.
Rhombus.
The answer is a rhombus.
Now let’s look at one other special quadrilateral.
A trapezoid is a quadrilateral that has only one pair of parallel sides.
Guided Practice
Identify the shape below as a rectangle, square, rhombus, or parallelogram.
First, check the lengths of the sides.
The opposite sides are congruent.
Next, check to see if the shape has four right angles.
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The shape has four right angles.
Then, identify the shape.
Rectangle.
The answer is rectangle.
Examples
Example 1
Identify each type of quadrilateral based on its description.
First, check the lengths of the sides.
The length of the sides is unknown, but the opposite sides appear to be congruent.
Next, check to see if the shape has four right angles.
The shape does not have four right angles.
Then, identify the shape.
Parallelogram.
The answer is parallelogram.
Example 2
A four sided figure with opposite sides parallel and congruent with four right angles.
First, check the number of sides.
The shape has four sides.
Next, note the relationship between the opposite sides.
The opposite sides are parallel and congruent.
Then, classify the shape.
Square.
The answer is a square.
Example 3
A four sided figure with two pairs of parallel sides. Opposite sides are congruent.
First, check the number of sides.
The shape has four sides.
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Chapter 1. Quadrilateral Classification
Next, note the relationship between the opposite sides.
The opposite sides are parallel and the parallel sides are congruent.
Then, classify the shape.
Parallelogram.
The answer is a parallelogram.
Follow Up
Remember Rasha and the door frame of her home? She paints a shape that has four sides and one set of parallel
sides. What shape is she painting?
First, check the number of sides.
The shape has four sides.
Next, check to see if the shape has parallel sides.
The shape has one set of parallel sides.
Then, identify the shape.
Trapezoid.
The answer is that Rasha is painting a trapezoid.
Video Review
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MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/166921
Explore More
Identify each quadrilateral as a parallelogram, rectangle, square, rhombus, or trapezoid.
1.
2.
3.
4.
Look at each image and name the quadrilateral pictured.
5.
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Chapter 1. Quadrilateral Classification
6.
7.
8.
9.
Name the geometric figure described below or answer each question.
10. Has four sides and four angles
11. Has one pair of opposite sides that are parallel
12. Has four right angles and four congruent sides
13. A parallelogram with four right angles.
14. A parallelogram with four congruent sides
15. Has four right angles and opposite sides congruent
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References
1. pixabay.com. https://pixabay.com/en/housewife-front-door-door-home-882533/ .
2. pixabay.com. https://pixabay.com/en/housewife-front-door-door-home-882533/ .
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