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 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), where a and b are the lengths of the other two sides.

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

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

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

In a right triangle, if the hypotenuse is 10 cm and one side is 6 cm, how do you find the length of the other side?

Back

Use the Pythagorean Theorem: a² + b² = c². Here, b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

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

If a right triangle has legs of lengths 5 cm and 12 cm, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 13 cm, calculated as: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

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.