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). Formula: a² + b² = c².

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse is a² + b² = c².

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 (3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What do the letters a, b, and c represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of the right triangle, and 'c' represents the length of the hypotenuse.

Front

How do you find the length of one side if you know the hypotenuse and one other side?

Back

You can find the length of one side using the formula: a² = c² - b² or b² = c² - a².

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 (10² - 6² = 100 - 36 = 64; √64 = 8).

Front

What is a right triangle?

Back

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

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to 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.