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 the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

If one side of a right triangle is 3 and the other side is 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 do you find a missing side of a right triangle using the Pythagorean Theorem?

Back

To find a missing side, rearrange the Pythagorean Theorem formula: a² = c² - b² or b² = c² - a², depending on which side is missing.

Front

If the hypotenuse is 10 and one side is 6, what is the length of the other side?

Back

The length of the other side is 8, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What are the conditions for using the Pythagorean Theorem?

Back

The Pythagorean Theorem can only be used for right triangles.

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.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

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