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 a² + b² = c².

Front

What does 'hypotenuse' mean?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If a = 9 and b = 40, what is c?

Back

c = 41, calculated using the Pythagorean Theorem: 9² + 40² = c².

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

How can you determine if a set of numbers can form a right triangle?

Back

Use the Pythagorean Theorem: check if a² + b² = c² for the largest number as c.

Front

Given the sides 20, 25, and 15, do they form a right triangle?

Back

Yes, because 15² + 20² = 25².

Front

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

Back

Use the Pythagorean Theorem: a² + b² = c², rearranging as needed.

Front

If one side is 12 and the hypotenuse is 40, what is the length of the other side?

Back

36, calculated using the Pythagorean Theorem.

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the hypotenuse.

Front

If a ladder reaches a height of 5 feet and the base is 7 feet from the wall, what is the length of the ladder?

Back

The length of the ladder (hypotenuse) is 11 feet, calculated using the Pythagorean Theorem.