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). Formula: a² + b² = c².

A right triangle is a triangle that has one angle measuring 90 degrees.

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

c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

The formula is a² + b² = c².

c = 13 (5² + 12² = 25 + 144 = 169, so c = √169 = 13).

Use the Pythagorean Theorem: if a² + b² = c² holds true, then the triangle is a right triangle.

The distance can be found using the Pythagorean Theorem, treating the two points as the endpoints of the legs of a right triangle.

10 blocks (using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so distance = √100 = 10).

The legs are the two sides that form the right angle.