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 sides a and b.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is denoted as side c.

Front

If a = 3 and b = 4, what is c?

Back

Using the Pythagorean Theorem: c² = a² + b²; c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

Is the statement 'a² + b² = c²' always true for right triangles?

Back

Yes, the statement 'a² + b² = c²' is always true for right triangles.

Front

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

Back

In a right triangle, the hypotenuse is always longer than either of the legs.

Front

If c = 10 and a = 6, what is b?

Back

Using the Pythagorean Theorem: b² = c² - a²; b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse is c = √(a² + b²).

Front

What is the formula to find the length of a leg if the hypotenuse and the other leg are known?

Back

The formula to find the length of a leg is a = √(c² - b²) or b = √(c² - a²).