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 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 one leg of a right triangle is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = √100 = 10 cm.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

The formula is c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

How do you find the length of a leg if you know the hypotenuse and one leg?

Back

Rearrange the Pythagorean theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

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 is 13 cm and one leg is 5 cm, what is the length of the other leg?

Back

Using the Pythagorean theorem: b² = 13² - 5²; b² = 169 - 25; b² = 144; b = √144 = 12 cm.

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 each leg.