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

What does the letter 'c' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse, which is the side opposite the right angle.

Front

If one side of a right triangle is 15 and the other side is 20, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 15² + 20²; c² = 225 + 400; c² = 625; c = 25.

Front

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

Back

To determine if three numbers can form a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers.

Front

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

Back

The formula is: a² + b² = c², where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5².

Front

What is the value of 'x' in the equation 21² - 15² = x²?

Back

x = √(21² - 15²) = √(441 - 225) = √216 = 14.7 (approximately).

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

Can the lengths 8, 15, and 17 form a right triangle?

Back

Yes, because 8² + 15² = 17² (64 + 225 = 289).