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: c² = a² + b².

Front

What is a right triangle?

Back

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

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.

Front

What is the hypotenuse of a right triangle?

Back

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

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 = 9 + 16 = 25; √25 = 5).

Front

How do you find the length of a missing leg in a right triangle?

Back

To find the length of a missing leg, rearrange the Pythagorean theorem: a² = c² - b² or b² = c² - a².

Front

What is the distance formula derived from the Pythagorean theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

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: 10² - 6² = 100 - 36 = 64; √64 = 8).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.