Quadrilaterals are a special kind of polygon. Similar to triangles and also other polygons, quadrilaterals have actually special properties and can be classified by qualities of their angles and sides. Expertise the properties of different quadrilaterals can assist you in solving difficulties that show off this form of polygon.

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Picking personally the name “quadrilateral” helps you understand what that refers to. The prefix “quad-” way “four,” and “lateral” is obtained from the Latin word for “side.” for this reason a square is a four-sided polygon.

Since the is a polygon, you know that that is a two-dimensional figure made up of right sides. A quadrilateral additionally has 4 angles formed by its 4 sides. Below are some examples of quadrilaterals. Notification that each figure has four straight sides and four angles.

The amount of the inner angles of any kind of quadrilateral is 360°. Think about the two examples below.

You could draw many quadrilaterals such as these and carefully measure up the 4 angles. Friend would uncover that because that every quadrilateral, the amount of the internal angles will constantly be 360°.

You can likewise use your understanding of triangles as a method to understand why the sum of the inner angles of any quadrilateral is 360°. Any type of quadrilateral can be split into two triangles as presented in the images below.

In the first image, the quadrilaterals have actually each been split into two triangles. The angle measurements of one triangle are displayed for each.

These measurements include up come 180º. Currently look at the dimensions for the various other triangles—they also add up to 180º!

Since the sum of the inner angles of any kind of triangle is 180° and also there are two triangles in a quadrilateral, the sum of the angle for each quadrilateral is 360°.

Specific types of Quadrilaterals

Let’s begin by evaluating the team of quadrilaterals that have two pairs of parallel sides. This quadrilaterals are dubbed parallelograms They take a selection of shapes, yet one classic example is shown below.

Imagine extending the bag of the opposite sides. Lock would never intersect since they are parallel. Notice, also, the the opposite angles of a parallelogram space congruent, as are the the opposite sides. (Remember the “congruent” means “the same size.”) The geometric symbol because that congruent is , for this reason you deserve to write

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

There room two special situations of parallelograms that will certainly be acquainted to friend from her earliest experiences through geometric shapes. The an initial special situation is dubbed a rectangle. By definition, a rectangle is a parallelogram due to the fact that its pairs of the contrary sides are parallel. A rectangle likewise has the one-of-a-kind characteristic that all of its angle are appropriate angles; all four of that is angles space congruent.

The other special instance of a parallelogram is a special form of rectangle, a square. A square is just one of the most simple geometric shapes. The is a special instance of a parallelogram that has four congruent sides and also four ideal angles.

A square is likewise a rectangle because it has two sets of parallel sides and four best angles. A square is also a parallelogram due to the fact that its the opposite sides are parallel. So, a square can be divide in any of these 3 ways, with “parallelogram” being the least details description and also “square,” the many descriptive.

Another quadrilateral that you can see is referred to as a rhombus. All 4 sides of a rhombus room congruent. Its properties encompass that each pair the opposite sides is parallel, likewise making that a parallelogram.

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

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

You can use the properties of parallelograms to settle problems. Consider the instance that follows.

 Example Problem Determine the procedures of  and . is the contrary  is opposite Identify the opposite angles. A building of parallelograms is that opposite angles are congruent. = 60°, for this reason  = 60°  = 120°, therefore  = 120° Use the provided angle measurements to recognize measures of the opposite angles. Answer = 60° and  = 120°

There is an additional special type of quadrilateral. This quadrilateral has actually the building of having actually only one pair the opposite sides that are parallel. Here is one example of a trapezoid.

Notice the

, and that  and  are no parallel. Girlfriend can easily imagine that if you extended sides and , they would intersect over the figure.

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

In this trapezoid ABCD,

and
.