Types of Triangles

1. Equilateral:

   • All sides are the same length.
   • Each angle is 60 degrees.

2. Isosceles:

   • Two sides are the same length.
   • The angles opposite those sides are also the same.

3. Scalene:

   • All sides and angles are different.

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Triangle Inequality Theorem

This rule says that if you have a triangle with three sides (let's call them a, b, and c), then:

1. The length of two sides added together must be bigger than the third side.
2. So you have to check these conditions:
   • a + b must be greater than c,
   • a + c must be greater than b,
   • b + c must be greater than a.

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Angle Sum Property

In any triangle, all the angles always add up to 180 degrees.

So, if you have angles A, B, and C, the formula looks like this:

• Angle A + Angle B + Angle C = 180 degrees.

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Pythagorean Theorem

This theorem is important for right triangles (triangles with one 90-degree angle).

Here’s the simplest way to state it:

• If you have two shorter sides, a and b, the longest side (called the hypotenuse, c) follows this rule:

• a² + b² = c².

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Area

You can find out how much space is inside a triangle using this formula:

• Area = 1/2 × base × height.

The base is one side of the triangle, and the height is how tall the triangle is from the base to the top point.