High School Mathematics - 2 8.14 Pythagorean Theorem - Examples

Theorem: In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides.
If the length of the hypotnuse is c and the lengths of other two sides are b and a then according to the pythogorean theorem: c^{2} = a^{2} + b^{2}

Converse: In a triangle if the square of one side is equal to the squares on the sums of the other two sides, then the angle opposite to the first side is a right angle.
To prove: AB^{2} + BC^{2} = AC^{2}

Example: Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of the diagonals.

Directions: Solve the following problems. Also write at least 10 examples of your own.