Quadrilaterals are a one-of-a-kind kind of polygon. As with triangles and also various other polygons, quadrilaterals have unique properties and also have the right to be classified by features of their angles and sides. Understanding the properties of different quadrilaterals have the right to help you in resolving problems that involve this form of polygon.

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Picking apart the name “quadrilateral” helps you understand also what it refers to. The presettle “quad-” means “four,” and also “lateral” is derived from the Latin word for “side.” So a quadrilateral is a four-sided polygon.

Due to the fact that it is a polygon, you know that it is a two-dimensional number consisted of of directly sides. A quadrilateral likewise has actually 4 angles created by its 4 sides. Below are some examples of quadrilaterals. Notice that each number has actually 4 directly sides and also 4 angles.

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The sum of the internal angles of any quadrilateral is 360°. Consider the 2 examples below.

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You might draw many quadrilaterals such as these and also carefully measure the 4 angles. You would uncover that for eincredibly quadrilateral, the sum of the inner angles will always be 360°.

You can also usage your expertise of triangles as a way to understand also why the amount of the inner angles of any kind of quadrilateral is 360°. Any quadrilateral have the right to be separated into 2 triangles as presented in the imeras below.

In the initially image, the quadrilaterals have actually each been separated right into 2 triangles. The angle measurements of one triangle are displayed for each.

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These measurements include up to 180º. Now look at the dimensions for the other triangles—they also include as much as 180º!

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Since the sum of the interior angles of any triangle is 180° and also tbelow are two triangles in a quadrilateral, the sum of the angles for each quadrilateral is 360°.


Specific Types of Quadrilaterals


Let’s begin by studying the group of quadrilaterals that have actually two pairs of parallel sides. These quadrilaterals are called parallelograms They take a selection of forms, however one timeless instance is shown listed below.

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Imagine extending the pairs of oppowebsite sides. They would never before intersect because they are parallel. Notice, likewise, that the opposite angles of a parallelogram are congruent, as are the opposite sides. (Remember that “congruent” suggests “the exact same dimension.”) The geometric symbol for congruent is , so you can compose

*
 and
*
. The parallel sides are also the same length:
*
 and also
*
. These relationships are true for all parallelograms.

There are two special instances of parallelograms that will certainly be familiar to you from your earliest experiences through geometric shapes. The first one-of-a-kind case is referred to as a rectangle. By interpretation, a rectangle is a parallelogram because its pairs of oppowebsite sides are parallel. A rectangle additionally has the unique characteristic that every one of its angles are ideal angles; all four of its angles are congruent.

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The other one-of-a-kind situation of a parallelogram is a distinct form of rectangle, a square. A square is just one of the the majority of fundamental geometric shapes. It is a special instance of a parallelogram that has 4 congruent sides and four best angles.

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A square is also a rectangle bereason it has actually two sets of parallel sides and also 4 right angles. A square is also a parallelogram bereason its opposite sides are parallel. So, a square have the right to be classified in any type of of these three ways, through “parallelogram” being the leastern certain description and “square,” the most descriptive.

Another quadrilateral that you might check out is called a rhombus. All four sides of a rhombus are congruent. Its properties encompass that each pair of opposite sides is parallel, also making it a parallelogram.

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In summary, all squares are rectangles, however not all rectangles are squares. All rectangles are parallelograms, however not all parallelograms are rectangles. And every one of these shapes are quadrilaterals.

The diagram listed below illustrates the partnership in between the various forms of quadrilaterals.

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You deserve to usage the properties of parallelograms to resolve difficulties. Consider the instance that complies with.


Example

Problem

Determine the procedures of

*
 and
*
.

*

 is opposite

 is opposite

Identify oppowebsite angles.

A residential property of parallelograms is that opposite angles are congruent.

*
 = 60°, so
*
 = 60°

*
 = 120°, so
*
 = 120°

Use the provided angle measurements to determine steps of opposite angles.

Answer

*
 = 60° and
*
 = 120°


Tbelow is another unique kind of quadrilateral. This quadrilateral has the residential or commercial property of having actually only one pair of oppowebsite sides that are parallel. Here is one instance of a trapezoid.

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Notice that

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, and that  and also  are not parallel. You have the right to conveniently imagine that if you extended sides and also , they would intersect above the figure.

If the non-parallel sides of a trapezoid are congruent, the trapezoid is called an isosceles trapezoid. Like the similarly called triangle that has 2 sides of equal size, the isosceles trapezoid has actually a pair of opposite sides of equal length. The various other pair of opposite sides is parallel. Below is an example of an isosceles trapezoid.

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In this trapezoid ABCD,

*
 and also
*
.

Which of the following statements is true?

A) Some trapezoids are parallelograms.

B) All trapezoids are quadrilaterals.

C) All rectangles are squares.

D) A form cannot be a parallelogram and a quadrilateral.


A) Some trapezoids are parallelograms.

Incorrect. Trapezoids have only one pair of parallel sides; parallelograms have actually 2 pairs of parallel sides. A trapezoid have the right to never before be a parallelogram. The correct answer is that all trapezoids are quadrilaterals.

B) All trapezoids are quadrilaterals.

Correct. Trapezoids are four-sided polygons, so they are all quadrilaterals.

C) All rectangles are squares.

Incorrect. Some rectangles might be squares, yet not all rectangles have 4 congruent sides. All squares are rectangles but. The correct answer is that all trapezoids are quadrilaterals.

D) A form cannot be a parallelogram and a quadrilateral.

Incorrect. All parallelograms are quadrilaterals, so if it is a parallelogram, it is likewise a quadrilateral. The correct answer is that all trapezoids are quadrilaterals.

You have the right to use the properties of quadrilaterals to settle troubles entailing trapezoids. Consider the instance below.


Example

Problem

Find the measure of

*
.

*

*
 = 360°

The sum of the steps of the internal angles of a quadrilateral is 360°.

*
 = 90°

*
 = 90°

The square symbol indicates a best angle.

60° +  + 90° + 90° = 360°

Because 3 of the 4 angle steps are offered, you deserve to discover the fourth angle measurement.

 + 240° = 360°

 = 120°

Calculate the measurement of

*
.

From the photo, you can view that it is an obtuse angle, so its meacertain need to be higher than 90°.

Answer

*
 = 120°


Name of Quadrilateral

Quadrilateral

Description

Parallelogram

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2 pairs of parallel sides.

Opposite sides and oppowebsite angles are congruent.

Rectangle

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2 pairs of parallel sides.

4 best angles (90°).

Opposite sides are parallel and also congruent.

All angles are congruent.

Square

*

4 congruent sides.

4 right angles (90°).

Oppowebsite sides are parallel.

All angles are congruent.

Trapezoid

*

Only one pair of oppowebsite sides is parallel.

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A quadrilateral is a mathematical name for a four-sided polygon. Parallelograms, squares, rectangles, and also trapezoids are all examples of quadrilaterals. These quadrilaterals earn their difference based upon their properties, including the number of pairs of parallel sides they have actually and also their angle and also side measurements.