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

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

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What are the lengths of the sides in a 5-12-13 triangle?

Back

The lengths of the sides are 5, 12, and 13, which form a right triangle.

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

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

Back

The formula is derived from the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) for one leg.

Front

If the lengths of two sides of a right triangle are 6 and 8, what is the length of the hypotenuse?

Back

10 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so c = √100 = 10).

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 right triangle has legs of lengths 9 and 12, what is the length of the hypotenuse?

Back

15 (Using the Pythagorean Theorem: 9² + 12² = 81 + 144 = 225, so c = √225 = 15).