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 is expressed as: a² + b² = c².

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle. It is denoted as 'c' in the Pythagorean Theorem.

Front

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

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5).

Front

If the hypotenuse of a right triangle is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

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

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Front

What is the formula for the Pythagorean Theorem?

Back

a² + b² = c².

Front

If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle?

Back

Yes, it is a right triangle (5² + 12² = 13²; 25 + 144 = 169).

Front

What happens if a² + b² < c² in a triangle?

Back

The triangle is obtuse.

Front

What happens if a² + b² > c² in a triangle?

Back

The triangle is acute.