# Scalene Triangle

## Definition

A triangle which has three unequal length sides, is called scalene triangle.

A triangle can have three unequal length sides but the meaning of scalene is unequal sides. Therefore, the name of scalene triangle is come to this triangle due to three unequal length sides.

In scalene triangle, the three interior angles are unequal mainly due to unequal length sides.

It is represented by a triangle with unequal length sides, which are indicated by single, double and triple minor lines perpendicularly at middle of the associated sides.

### Properties

The $\Delta OPQ$ is an example for scalene triangle to study its fundamental properties.

#### Sides

$\overline{OP}$, $\overline{PQ}$ and $\overline{QO}$ are three sides but the lengths of them are different.

$OP \neq PQ \neq QO$

The triangle is known as scalene triangle due to unequal length sides.

#### Angles

The triangle contains three interior angles but they are not equal angles. It is mainly due to unequal length three sides.

$\angle OPQ \neq \angle PQO \neq \angle QOP$

##### Construction

A scalene triangle can be constructed in geometry by using geometric tools and it helps us to study the properties understandably.

1. Draw a horizontal line of any length by using a ruler. Here, $10$ centimetres line has drawn and its endpoints are called as point $R$ and point $S$.
2. Take compass and consider measuring system of ruler to set the distance between pencil lead point and needle point to any length ($7$ centimetres is set in this example). Then draw an arc from point $R$ above the horizontal line $\overline{RS}$.
3. Again use compass and set the distance of two points to any length (For example $5$ centimetres). Now, draw an arc from point $S$ above the horizontal line. The two arcs intersect each other at point $T$.
4. Join points $R$ and $T$ and then $S$ and $T$ using ruler.

According to this step by step process, the $\Delta RST$ is constructed geometrically. The points $R$, $S$, and $T$ become its vertices and $\overline{RS}$, $\overline{ST}$ and $\overline{TR}$ are called as its sides.

1
###### Lengths of sides

The triangle $RST$ is constructed geometrically by the known lengths.

1. The length of the side $\overline{RS}$ is $RS = 10$ Centimetres.
2. The length of the side $\overline{ST}$ is $ST = 5$ Centimeters.
3. The length of the side $\overline{TR}$ is $TR = 7$ Centimetres.

The lengths of all three sides are different. Hence, the triangle is an example to the scalene triangle.

2
###### Angles

The three interior angles of $\Delta RST$ are unknown but they can be measured by a protractor.

1. The angle $TRS$ ($\angle TRS$) is measured as $27.5^\circ$.
2. The angle $RST$ ($\angle RST$) is measured as $40.5^\circ$.
3. The angle $STR$ ($\angle STR$) is measured as $112^\circ$.

The three interior angles of this triangle are different. It is chiefly due to the formation of the $\Delta RST$ by the three unequal length line segments.