There are three types of triangles based on how many sides or angles that are equal. Those are, the Equilateral Triangle with all three sides equal, and all angles equal (always 60°), the Isosceles Triangle with all two sides equal and two angles equal, and lastly, the Scalene Triangle with none of the sides equal and none of the angles equal.

### Equilateral Triangle

### Isosceles Triangle

### Scalene Triangle

Once we classify the triangle, we can use this information to solve for missing sides/angles.

## Sum of Interior Angles

In a triangle, the three interior angles always add to 180°:

\(\angle A + \angle B + \angle C = 180°\)

Refer to the diagram below. A triangle with angles \(\angle A,\ \angle B\) and \(\angle C\) is extended with a parallel line \(\vec{DE}\),
such that \(\vec{AC}\) is parallel to \(\vec{DE}\).
From this we can use a "Z" pattern rule to see that the three angles make a straight line around point B. We know that a straight line is 180° so the sum of the interior angles of the triangle must also be 180°!

An equilateral triangle has side lengths \(a=3\) and \(b=3\). Calculate the missing length.

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In an equilateral triangle, all three sides are the same. Thus,

\( c = 3\)

In a scalene triangle, one angle is 116 degrees, another is 35 degrees. What's the degree of the third angle?"

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The sum of interior angles in any triangle is 180:

\(\angle A + \angle B + \angle C = 180°\)

\(116 + 35 + \angle C = 180\)

\(\angle C = 180 - 116 - 35\)

\(\angle C = 29\)

If the height of an equilateral triangle is 2√3. Calculate the side length.

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To solve this problem we first define the side length of the equilateral triangle as \(x\). Each side is the same and we know the height.
We can focus on half the equilateral triangle with base \(x/2\), height \( h = 2\sqrt{3}\) and hypoteneus \(x\). This is a right angle so we can use the Pythagorean Theorem!

\(x^2=(\cfrac{x}{2})^2+ (2√3)^2\)

\(x^2=\cfrac{x^2}{4}+ 12\)

\(\cfrac{3x^2}{4} = 12\)

\(x^2 = 16\)

\(x = 4\)

The side length of the triangle is \(x = 4\).