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

Back

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

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 5, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides (a and b) add up to the square of the length of the longest side (c). If a² + b² = c², it is a right triangle.

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

If the sides of a triangle are 5, 12, and 13, is it a right triangle?

Back

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

Front

What is the relationship between the sides in the Pythagorean Theorem?

Back

The relationship is expressed as: a² + b² = c².

Front

What is the length of the diagonal of a rectangle with sides 12 inches and 17 inches?

Back

The length of the diagonal is approximately 20.8 inches, calculated as: d = √(12² + 17²) = √(144 + 289) = √433 ≈ 20.8.

Front

What does 'hypotenuse' mean?

Back

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