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

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Picking acomponent the name “quadrilateral” helps you understand also what it describes. The preresolve “quad-” means “4,” and “lateral” is acquired from the Latin word for “side.” So a quadrilateral is a four-sided polygon.

Since it is a polygon, you recognize that it is a two-dimensional number consisted of of right sides. A quadrilateral additionally has actually four angles formed by its 4 sides. Below are some examples of quadrilaterals. Notice that each number has actually 4 straight sides and 4 angles.

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The amount of the interior angles of any type of quadrilateral is 360°. Consider the 2 examples listed below.

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You can draw many quadrilaterals such as these and closely measure the 4 angles. You would certainly uncover that for eextremely quadrilateral, the amount of the internal angles will certainly always be 360°.

You can likewise use your expertise of triangles as a way to understand why the sum of the interior angles of any type of quadrilateral is 360°. Any quadrilateral have the right to be divided right into two triangles as presented in the images listed below.

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

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

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Since the amount of the inner angles of any type of triangle is 180° and there are 2 triangles in a quadrilateral, the sum of the angles for each quadrilateral is 360°.


Specific Types of Quadrilaterals


Let’s begin by examining the group of quadrilaterals that have actually two pairs of parallel sides. These quadrilaterals are dubbed parallelograms They take a variety of shapes, however one timeless example is displayed listed below.

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Imagine extfinishing 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 oppowebsite sides. (Remember that “congruent” indicates “the exact same size.”) The geometric symbol for congruent is , so you can write

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

Tright here are 2 distinct instances of parallelograms that will certainly be familiar to you from your earliest experiences with geometric shapes. The initially one-of-a-kind situation is referred to as a rectangle. By interpretation, a rectangle is a parallelogram because its pairs of oppowebsite sides are parallel. A rectangle likewise has the one-of-a-kind characteristic that every one of its angles are right angles; all four of its angles are congruent.

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The various other unique instance of a parallelogram is a distinct form of rectangle, a square. A square is just one of the many basic geometric shapes. It is a one-of-a-kind situation of a parallelogram that has actually 4 congruent sides and also four best angles.

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A square is likewise a rectangle bereason it has actually two sets of parallel sides and 4 ideal angles. A square is likewise a parallelogram bereason its opposite sides are parallel. So, a square deserve to be classified in any type of of these 3 methods, via “parallelogram” being the leastern certain summary and “square,” the many descriptive.

Another quadrilateral that you can watch is referred to as a rhombus. All 4 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, but not all rectangles are squares. All rectangles are parallelograms, however not all parallelograms are rectangles. And every one of these forms are quadrilaterals.

The diagram below illustprices the partnership in between the various types of quadrilaterals.

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You have the right to use the properties of parallelograms to solve troubles. Consider the example that follows.


Example

Problem

Determine the actions of

*
 and
*
.

*

 is opposite

 is opposite

Identify oppowebsite angles.

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

*
 = 60°, so
*
 = 60°

*
 = 120°, so
*
 = 120°

Use the offered angle measurements to identify actions of oppowebsite angles.

Answer

*
 = 60° and
*
 = 120°


Tbelow is one more distinct type of quadrilateral. This quadrilateral has the home of having actually only one pair of opposite sides that are parallel. Here is one instance of a trapezoid.

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Notice that

*
, and that  and  are not parallel. You deserve to easily imagine that if you extended sides and also , they would certainly intersect over the number.

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

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In this trapezoid ABCD,

*
 and
*
.

Which of the complying with statements is true?

A) Some trapezoids are parallelograms.

B) All trapezoids are quadrilaterals.

C) All rectangles are squares.

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


A) Some trapezoids are parallelograms.

Incorrect. Trapezoids have only one pair of parallel sides; parallelograms have actually two pairs of parallel sides. A trapezoid can never 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 may be squares, however not all rectangles have four congruent sides. All squares are rectangles yet. The correct answer is that all trapezoids are quadrilaterals.

D) A shape 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 deserve to usage the properties of quadrilaterals to fix troubles entailing trapezoids. Consider the instance below.


Example

Problem

Find the meacertain of

*
.

*

*
 = 360°

The amount of the actions of the inner angles of a quadrilateral is 360°.

*
 = 90°

*
 = 90°

The square symbol shows a appropriate angle.

60° +  + 90° + 90° = 360°

Since three of the four angle measures are provided, you deserve to find the fourth angle measurement.

 + 240° = 360°

 = 120°

Calculate the measurement of

*
.

From the picture, you can watch that it is an obtuse angle, so its measure have to be greater than 90°.

Answer

*
 = 120°


Name of Quadrilateral

Quadrilateral

Description

Parallelogram

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2 pairs of parallel sides.

Oppowebsite sides and also opposite angles are congruent.

Rectangle

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2 pairs of parallel sides.

4 right angles (90°).

Opposite sides are parallel and congruent.

All angles are congruent.

Square

*

4 congruent sides.

4 best angles (90°).

Oppowebsite sides are parallel.

All angles are congruent.

Trapezoid

*

Only one pair of opposite sides is parallel.

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