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

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

In the Pythagorean Theorem, a and b represent the lengths of the two legs of the right triangle.

5 units (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

False. The legs can be of different lengths.

The area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

8 units (Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the legs.

The right angle (90 degrees) is the angle that defines a right triangle and is essential for applying the Pythagorean Theorem.

√(5² + 5²) = √(25 + 25) = √50 ≈ 7.07 units.