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 is expressed as: c² = a² + b².

Front

Is the statement a² + b³ = c⁴ true or false?

Back

False. The correct form is a² + b² = c².

Front

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

Back

c = √(a² + b²) where c is the hypotenuse and a and b are the other two sides.

Front

What is the opposite of squaring a number?

Back

Square root.

Front

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

Back

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

Front

Do the lengths 6, 8, and 10 form a right triangle?

Back

Yes, they do (6² + 8² = 10²).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If one side of a right triangle is 5 and the hypotenuse is 13, what is the length of the other side?

Back

12 (using the Pythagorean Theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12).

Front

What does it mean for a triangle to be 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.