Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as: c² = a² + b².

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.

No, the Pythagorean Theorem only applies to right triangles.

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², depending on which side is missing.

It is an isosceles right triangle.

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.

The converse states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.