Pythagorean Theorem - Converse

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). It can be expressed as: c² = a² + b².

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

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Use the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

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.

Yes, because 7² + 24² = 25² (49 + 576 = 625).

The distance between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Use the Pythagorean Theorem: c² = 30² + 15²; c² = 900 + 225; c = √1125 ≈ 33.5 feet.

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.