Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

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.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

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

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

In a right triangle, if one side is 6 cm and the hypotenuse is 10 cm, what is the length of the other side?

Back

8 cm (using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8).

Front

What is the formula to find the length of a side in a right triangle?

Back

The formula is c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has sides of length 5 cm and 12 cm, what is the length of the hypotenuse?

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

The sum of the squares of the two shorter sides equals the square of the hypotenuse.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

26 feet (using the Pythagorean Theorem: 10² + 24² = 100 + 576 = 676, so the ladder length is √676 = 26).

Front

What is the Pythagorean triplet?

Back

A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c². Example: (3, 4, 5).