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: c² = a² + b².

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 formula to find the hypotenuse in a right triangle?

Back

The formula to find the hypotenuse (c) is: c² = a² + b².

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The relationship is that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Is the statement 'c² = a² - b²' true or false?

Back

False. The correct formula is c² = a² + b².

Front

What does the term 'hypotenuse' refer to?

Back

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

Front

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

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

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

Back

Using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = 8.

Front

What is the formula to find one leg if the hypotenuse and the other leg are known?

Back

If c is the hypotenuse and a is the known leg, then b can be found using: b² = c² - a².