What is a 90 Degree Angle

Squares have many different properties. These properties are how you can recognize if a shape is a square or not. In order to understand these properties, let’s first take a look at the concepts behind them.The first concept you need to understand is what a 90 degree angle is. Take a look at the definition of an angle.

 

angle_definition
Definition Measurement Notation
Angle The corner formed by two lines Degrees angle{X}

 

As you can see in the table above, an angle is usually given in degrees. There are many different types of angles that can be formed by two lines. Take a look at some of the common ones below.

 

acute_and_obtuse
Acute Angle Obtuse Angle
Degrees 0-89 91-180

 

A 90 degree angle is exactly what it sounds like - it is an angle that equals 90 degrees. It is known as a right angle.

 

right_angle_definition

 

Right Angle Notation
Degrees 90 degrees Small square

 

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What are Parallel Lines

Parallel lines are one of the common types of lines. Take a look at the table below for the definition.

 

parallel_lines_notation

 

Definition Notation Notation on the line
Parallel Lines Two lines that never touch and are always the same distance apart overline{AB} ; || ; overline{CD} Arrows that are the same number

 

What are Congruent Lines

In order to understand what congruent lines are, we should specify that we’re really talking about line segments. Take a look at the differences in definitions below.

 

Line Line Segment
A straight line that goes to infinity in both directions A part, or segment, of a line.

 

The definition and notation of a line segment is below.

 

Definition Notation
Congruent Two line segments that have the same length Matching dashes on the line segments

 

We can look at some examples below.

 

rectangle_notation
A B
overline{AB} ; = ; overline{CD} overline{EF} ; = ; overline{GH}

 

Definition of Square

Now that you understand some of these basic concepts, let’s take a look at the definition of a square.

 

Definition
Square A square is a quadrilateral that has four sides that are congruent and has four right angles.

 

Let’s take a look at this definition and how the notation on the square looks like.

 

square_notation

 

No matter what the size of a square is, all squares have the same basic properties. Let’s take a look at some of these properties.

Property 1 All touching line segments are perpendicular to each other
Property 2 Opposite line segments are parallel

 

Parallelogram

A square is a part of the parallelogram family. Parallelograms are shapes that can be classified by specific properties. Let’s take a look at these properties.

 

Property 1 Is a plane figure, which is a two dimensional figure with no thickness
Property 2 Made up of 3 or more line segments
Property 3 Has four sides
Property 4 Each opposite side is parallel to each other
Property 5 Each opposite side is congruent

 

The first 2 properties make up the definition of a polygon, while the combination of the first 3 properties make up the definition of a quadrilateral. There are 3 major types of parallelograms, which you can see in the image below.

 

paralellogram_shapes
A B C
Rectangle Square Rhombus

 

Diagonal of a Square

An additional property of a square can be seen in its diagonal. The diagonal of a square is simply the line that connects each opposite angle. There are two major properties you should know about the diagonal of a square. Take a look at the first one below.

 

square_diagonals
Description
Diagonal The two diagonals of a square are perpendicular bisectors
Perpendicular bisector Two lines that are perpendicular at the midpoint of the line

 

The second property can be described below in the table.

 

diagonal_bisectors

 

Description
Diagonal The diagonals bisect the angles of each corner
Bisecting angles When angles are cut directly in half

 

Perimeter of Square

The perimeter of any shape is the total length of the boundary of the shape. Take a look at an example below.

perimeter_shape
Notation Example
Perimeter P P = 3+2+1+2+1

 

Since a square has four equal sides (s), the perimeter of a square can be found by either of the following two formulas.

 

Equation 1 Equation 2
Perimeter P = s+s+s+s P = 4*s

 

Area of a Square

The area of any shape is the size of the surface contained inside of any boundary. Because you want to be able to compare the areas of all shapes, regardless of what they are, the area is calculated in square units.

 

Definition Use
Square Unit A square with each side equal to 1 unit Can compare how many square units are contained in each shape

 

The area of a square can be found by simply finding the square of one side. The reason why is explained in the table below.

 

A square has four equal sides Sides equal length of s
Square units can be found by multiplying the length times width l*w
The length and width of a square are equal to each other l = w = s
The area is the square of one side A = s*s = s^{2}

 

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Danica

Located in Prague and studying to become a Statistician, I enjoy reading, writing, and exploring new places.