Quadrilaterals space a special form of polygon. Similar to triangles and other polygons, quadrilaterals have special properties and also can it is in classified by qualities of your angles and also sides. Understanding the properties of various quadrilaterals can aid you in solving troubles that indicate this form of polygon.

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Picking personally the surname “quadrilateral” help you recognize what the refers to. The prefix “quad-” method “four,” and also “lateral” is obtained from the Latin word for “side.” so a quadrilateral is a four-sided polygon.

Since that is a polygon, you know that it is a two-dimensional figure comprised of straight sides. A quadrilateral likewise has 4 angles formed by its 4 sides. Listed below are some instances of quadrilaterals. An alert that each figure has 4 straight sides and four angles.

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The amount of the inner angles of any type of quadrilateral is 360°. Take into consideration the two instances below.

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You can draw plenty of quadrilaterals such together these and carefully measure the four angles. You would uncover that because that every quadrilateral, the amount of the inner angles will always be 360°.

You can likewise use your expertise of triangles as a way to recognize why the sum of the internal angles of any kind of quadrilateral is 360°. Any quadrilateral have the right to be separated into 2 triangles as presented in the photos below.

In the an initial image, the quadrilaterals have each been split into two triangles. The angle dimensions of one triangle are shown for each.

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These measurements add up to 180º. Now look in ~ the dimensions for the other triangles—they also include up to 180º!

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Since the sum of the internal angles of any triangle is 180° and there are two triangle in a quadrilateral, the sum of the angles for each square is 360°.


Specific types of Quadrilaterals


Let’s begin by analyzing the group of quadrilaterals that have actually two bag of parallel sides. These quadrilaterals are referred to as parallelograms They take a selection of shapes, but one standard example is shown below.

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Imagine expanding the bag of opposite sides. They would never intersect due to the fact that they are parallel. Notice, also, the the opposite angle of a parallelogram space congruent, as room the the opposite sides. (Remember the “congruent” way “the exact same size.”) The geometric symbol for congruent is , therefore you deserve to write

*
 and
*
. The parallel sides are likewise the same length:
*
 and
*
. These relationships room true for every parallelograms.

There are two special cases of parallelograms that will certainly be familiar to friend from her earliest experiences v geometric shapes. The an initial special situation is referred to as a rectangle. By definition, a rectangle is a parallelogram because its pairs of the contrary sides space parallel. A rectangle additionally has the one-of-a-kind characteristic that all of its angle are best angles; all 4 of the angles room congruent.

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The various other special instance of a parallel is a special kind of rectangle, a square. A square is among the most straightforward geometric shapes. That is a special situation of a parallelogram that has four congruent sides and four right angles.

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A square is likewise a rectangle because it has two to adjust of parallel sides and also four ideal angles. A square is likewise a parallelogram since its the contrary sides room parallel. So, a square have the right to be divide in any kind of of these 3 ways, through “parallelogram” being the least details description and “square,” the many descriptive.

Another quadrilateral the you might see is called a rhombus. All four sides of a rhombus room congruent. That properties include that each pair the opposite political parties is parallel, also making the a parallelogram.

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In summary, all squares are rectangles, however not all rectangles room squares. Every rectangles room parallelograms, but not all parallelograms space rectangles. And every one of these forms are quadrilaterals.

The diagram below illustrates the relationship between the different types of quadrilaterals.

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You deserve to use the properties of parallelograms to fix problems. Think about the example that follows.


Example

Problem

Determine the procedures of

*
 and
*
.

*

 is the opposite

 is opposite

Identify the contrary angles.

A residential or commercial property of parallelograms is that opposite angles space congruent.

*
 = 60°, therefore
*
 = 60°

*
 = 120°, therefore
*
 = 120°

Use the offered angle dimensions to determine measures of the opposite angles.

Answer

*
 = 60° and
*
 = 120°


There is an additional special type of quadrilateral. This quadrilateral has actually the residential property of having only one pair that opposite sides that are parallel. Below is one instance of a trapezoid.

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Notice that

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, and that  and  are not parallel. You can quickly imagine that if you prolonged sides and also , they would intersect above the figure.

If the non-parallel sides of a trapezoid space congruent, the trapezoid is called an isosceles trapezoid. Choose the likewise named triangle that has two political parties of equal length, the isosceles trapezoid has actually a pair that opposite sides of same length. The various other pair the opposite political parties is parallel. Below is an example of one isosceles trapezoid.

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In this trapezoid ABCD,

*
 and
*
.

Which the the following statements is true?

A) some trapezoids room parallelograms.

B) every trapezoids are quadrilaterals.

C) every rectangles are squares.

D) A shape cannot it is in a parallelogram and also a quadrilateral.


A) part trapezoids are parallelograms.

Incorrect. Trapezoids have actually only one pair the parallel sides; parallelograms have actually two bag of parallel sides. A trapezoid have the right to never it is in a parallelogram. The exactly answer is the all trapezoids are quadrilaterals.

B) every trapezoids room quadrilaterals.

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

C) every rectangles space squares.

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

D) A form cannot it is in a parallelogram and a quadrilateral.

Incorrect. Every parallelograms space quadrilaterals, for this reason if it is a parallelogram, the is likewise a quadrilateral. The correct answer is the all trapezoids are quadrilaterals.

You have the right to use the nature of quadrilaterals to solve problems involving trapezoids. Take into consideration the instance below.


Example

Problem

Find the measure of

*
.

*

*
 = 360°

The sum of the steps of the interior angles that a square is 360°.

*
 = 90°

*
 = 90°

The square symbol shows a right angle.

60° +  + 90° + 90° = 360°

Since 3 of the four angle actions are given, you can uncover the 4th angle measurement.

 + 240° = 360°

 = 120°

Calculate the measurement of

*
.

From the image, you can see the it is one obtuse angle, for this reason its measure must be better than 90°.

Answer

*
 = 120°


Name the Quadrilateral

Quadrilateral

Description

Parallelogram

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2 pairs of parallel sides.

Opposite sides and also opposite angles space congruent.

Rectangle

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2 pairs of parallel sides.

4 best angles (90°).

Opposite sides room parallel and congruent.

All angles room congruent.

Square

*

4 congruent sides.

4 right angles (90°).

Opposite sides room parallel.

All angles are congruent.

Trapezoid

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Only one pair that opposite sides is parallel.

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A quadrilateral is a mathematical surname for a four-sided polygon. Parallelograms, squares, rectangles, and trapezoids are all examples of quadrilaterals. These quadrilaterals knife their difference based on their properties, consisting of the variety of pairs the parallel political parties they have and their angle and side measurements.