## What is a Triangle?

### Triangle- Definition

Any flat polygon (two dimensional) that is enclosed with three straight lines is called a triangle.

- The sum of the three angles inside the triangle always will add up to 180 degrees.
- The area of a triangle is ½ base *height (the length which is at 90 degrees to the base). Why? If you flip the triangle and make it double, you will get a parallelogram whose area is base*height.
- There is a mysterious triangle in the Atlantic Ocean called the Bermuda Triangle where planes disappear and UFOs have also been spotted there.
- Why are most pizzas cut into triangle shapes? That is the only way a circle can be equally cut.
- Pascal’s Triangle named after Blaise Pascal is a triangle where each number inside the triangle is the sum of the two numbers above it.
- Crayons have a triangular shape at the top to better guide the artist in getting a more firm grip over the crayon.

## Different Types of Triangles

### Triangles according to the Internal Angles-

**Right Angle Triangle or 45-45-90 Triangle**

- One angle is 90° and the side opposite to is called hypotenuse and the other sides are catheti.
- It is used in the Pythagoras Theorem where if we place three squares on each side of the triangle, the largest square will always be equal to the area of the other two squares.
- Isosceles right angled triangle has two equal angles of 45° and two equal sides.
- Scalene right angled triangle has no equal sides or angles. A 30-60-90 triangle is a specific case of a scalene right angles triangle.

**Acute Triangle**

Each angle is less than 90° and the sum of any two angles is always greater than 90°.

Examples: A doctor’s stethoscope has acute angles, arrows for one way and no right turn contain acute angles, top of the letter A or the top of a football has an acute angle.

**Obtuse Triangle**

One angle in the triangle is greater than 90°. They are called dull angles.

Examples: Boomerangs, roof tops

## Triangles according to their Sides

**A Scalene Triangle** is a triangle that does not have equal sides. The longest side of the triangle is right across from the longest angle and so forth. A scalene triangle shape is powerful and strong and thus used to design roofs or ramps in a skateboard park or the sail of a sailboat.

**An Isosceles Triangle** is a triangle which has two equal angles and sides.

Examples: a pizza slice, a cake slice, a pennant, a flock of birds flying in an isosceles triangle shape. Guyana’s flag has an isosceles triangle on it. Futuristic planes use isosceles triangles as it reduces drag and increases lift.

**An Equilateral Triangle** is a triangle with equal sides and equal angles (each angle is 60°).

**Similar Triangles** are alike in all respects except size. So their angles are equal and their sides are in the same ratio.

**Congruent Triangles** are exactly same to each other, both in terms of angles and sides.

## Other Properties of Triangles

- The Incenter of a triangle is where the three angle bisectors meet. From this point any circle that is drawn and touches the three sides of the triangle is the largest circle.
- The Circumcenter of a triangle is where the perpendicular bisectors criss cross. Each perpendicular bisector cuts another line into two equal parts and at 90°.

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