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: a² + b² = c².

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 side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. If a² + b² = c², then it is a right triangle.

Front

What are the side lengths of a right triangle called?

Back

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

Front

If a triangle has sides of lengths 6, 8, and 10, is it a right triangle?

Back

Yes, because 6² + 8² = 36 + 64 = 100, which equals 10².

Front

What is the length of the diagonal of a rectangle with sides 3 cm and 4 cm?

Back

The length of the diagonal can be found using the Pythagorean theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Front

Can a triangle with sides 5, 12, and 13 be a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which equals 13².

Front

What is the relationship between the sides of a right triangle and the Pythagorean theorem?

Back

The Pythagorean theorem provides a relationship between the lengths of the sides of a right triangle, allowing us to calculate one side if the other two are known.

Front

If a triangle has sides of lengths 7, 24, and 25, what can you conclude about it?

Back

It is a right triangle because 7² + 24² = 49 + 576 = 625, which equals 25².

Front

What is the formula to find the hypotenuse of a right triangle?

Back

The formula to find the hypotenuse (c) is c = √(a² + b²), where a and b are the lengths of the other two sides.