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: a² + b² = c².

Front

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

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

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

Back

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

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if it has one angle that measures 90 degrees and satisfies the Pythagorean Theorem.

Front

Which set of sides can form a right triangle? 5, 12, 13 or 8, 10, 12?

Back

The set 5, 12, 13 can form a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides.

Front

What is the length of the diagonal of a rectangle with length 40 yards and width 30 yards?

Back

Using the Pythagorean Theorem: diagonal = √(40² + 30²) = √(1600 + 900) = √2500 = 50 yards.

Front

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

Back

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

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Can a triangle with sides 7, 24, and 25 be a right triangle?

Back

Yes, because 7² + 24² = 25² (49 + 576 = 625).