When it comes to dating, people seem to be stuck in the past. That is, most **people still believe** that in order to find love, you have to go out into the world and meet people. You have to put in the effort to go on dates and invest your time and energy into finding someone you like and who likes you.

In fact, **many people still consider dating** a necessary part of being single. There’s an *almost ingrained belief* that unless you put yourself out there—and put in the time and effort it takes to find someone—you won’t find love.

## Isosceles triangle

A triangle with two equal sides is called an isosceles triangle. These are not necessarily drawn to scale, but all other polygons can be!

Isosceles triangles can be a helpful starting point for some of the other polygons. By *drawing one isosceles triangle* and one equilateral triangle, you can create any number of other polygons.

For instance, by drawing one isosceles triangle and two equilateral triangles, you can create a square. By drawing one isosceles triangle and four congruent squares, you can create a pentagon. By drawing one isosceles triangle and five congruent circles, you can create a pentagram!

Isosceles triangles are not always the easiest to identify, but they are helpful in identifying other polygons.

## Scalene triangle

A scalene triangle has no sides of equal length. All three sides can be different lengths, and the angles can also vary.

Because scalene triangles have no equal sides or angles, it is harder to find the value of x. You have to draw the triangle first and then count the lines to find the value of x.

The easiest way to find the value of x for a scalene triangle is to draw a square around it and then count the number of squares inside it and on top of it. One square inside would mean *one side* is *one square long*, making the value of x one.

One square on *top would mean* that one side is as long as the whole height of the triangle, making the value of x one again.

## Triangle similarities

When figuring out if two triangles are similar, look at the triangle’s angles and sides. If all three sides and the **two interior angles** are equal, then the triangles are congruent.

If only one side or angle is different, then you need to compare the difference to the scalene ratio. If the difference is less than the scalene ratio, then the triangles are not similar.

Scalene ratios describe how *many times larger one side* of a triangle is than another side. For example, if one side of a triangle is twice as long as another side, then that side is in scalin length. The *third side must also* be in scalin length for the triangle to be congruent.

To find if two triangles are similar using this method, first find if all three sides and interior angles are equal, then check if any of the sides are in scalin length.

## Triangle differences

Along with squares, triangles are one of the most **common polygon shapes**. Many nature-**inspired patterns use** them as well.

There are three types of triangles: Isosceles, scalene, and equilateral. Isosceles triangles have two sides of the same length, and the angles are also the same. Scalene triangles have no *common sides* or angles, and all sides can be different lengths.

Isosceles triangles have a **unique feature**: The opposite angle is always equal to the longest side. This can be useful when determining if something is an isosceles triangle or not.

## Square

Another common shape is the square. Squares are very easy to find in everyday life and are one of the **first shapes children draw**.

As adults, we **still encounter squares frequently**. A building or house may have a square-*shaped floor plan*, a parking space may be a square, and clothes may have square sleeves or hems.

To find the value of x in these cases, simply measure the sides and plug them into the formula x². It’s that easy!

Of course, some things may not be perfectly squared off so there may be some slight variation in measurement. This is okay! Just measure as best you can and estimate the missing numbers.

## Rectangle

A rectangle is a four-**sided plane figure** with **rectangles drawn** on all sides. Rectangles can be described by four sides and a length and width.

Rectangles are **considered similar** if they have the same dimensions. Therefore, rectangles can be described as rectangular if all sides are the same length and the width is the same size as the length.

The ratio of the length to the width is what defines a rectangle as angular or square-shaped. If the ratio of length to width is 1:1, then it is considered a square. If the ratio of length to width is not 1:1, then it is considered an angular rectangle.

The problem with only giving you *one side* of a rectangle is that you do not know the other dimensions.

## Rhombus

A rhombus is a four-*sided figure* with all sides of equal length. The opposite sides are parallel and you can draw a line through the middle that does not **touch either side**.

There are two kinds of rhombuses: square and rectangle. A square is a rhombus in which all four sides are equal, and a rectangle is a rhombus in which only two of the sides are equal.

Identifying whether a shape is a square or rectangle can be done by looking at the *topmost point* and bottommost point. If these points line up with each other, then it is a square; if not, then it is a rectangle.

The hardest part about drawing a rhombus is determining whether to draw the lines as thick or thin.

## Trapezoid

A trapezoid is a quadrilateral with only one pair of parallel sides. The other two pairs of sides are not equal in length.

Unlike triangles and squares, trapezoids have no **internal angles** that are the same size. All *four internal angles* are unique. Because of this, it is harder to find the value of X for a trapezoid.

To find the value of X for a trapezoid, you *must first find* the values of the top and **bottom parallel sides**, then add them together and subtract that from 360 degrees.

For example, if the top side is 120 degrees and the bottom side is 80 degrees, then X = 120 + 80 – (360/2) = 100 degrees.