## The Pythagorean Theorem

In an isosceles triangle, the two sides that are equal to each other are also equal to the square root of the hypotenuse.

### Identify a right triangle

A right triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The side opposite the right angle is called the hypotenuse, and the other two sides are called legs.

### Find the length of the hypotenuse.

Given a right triangle with sides of lengths a and b, the length of the hypotenuse c can be found using the Pythagorean theorem:

c^2 = a^2 + b^2

This theorem is represented by the following equation:

c = √(a^2 + b^2)

This equation says that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, if you know the lengths of two sides of a right triangle, you can find the length of the third side using this equation.

### Use the Pythagorean Theorem to find the length of the other two sides

The Pythagorean Theorem is one of the most famous geometric theorems. The theorem states that in a right angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

This theorem can be used to find the length of any one of the sides in a right angled triangle, if you know the lengths of the other two sides.

## The Isosceles Triangle

An isosceles triangle is a triangle with (at least) two equal sides. The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the third side. This is because the two sides of an isosceles triangle are equal.

### Find the length of one of the sides

If you know the length of two sides of an isosceles triangle, you can find the length of the third side with the following formula:

Side^2 = (Length of Side 1)^2 + (Length of Side 2)^2 – 2 * (Length of Side 1) * (Length of Side 2) * cos(angle between sides)

You will need to know the measure of the angle between the two sides in order to use this formula.

### Find the length of the other side

An isosceles triangle is a triangle with (at least) two equal sides. This means that if you know the length of one of the sides and one of the angles, you can find the lengths of the other two sides. Let’s say that we have an isosceles triangle where Side A is equal to Side B, and we know that Angle C equals 90 degrees. We can use basic trigonometry to find that Side C must equal Side A times the cosine of Angle A.

### Use the Pythagorean Theorem to find the length of the hypotenuse

The Pythagorean Theorem is one of the most famous geometric theorems. The theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is represented by the equation:

a^2 + b^2 = c^2

Where a and b are the lengths of the shorter sides of the triangle and c is the length of the hypotenuse. In order to use this theorem to find the length of the hypotenuse, you need to know either:

-the lengths of both shorter sides OR

-the length of one shorter side and the value of c