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 hypotenuse in a right triangle?

Back

The formula to find the hypotenuse (c) is: c = √(a² + b²).

Front

What is the hypotenuse in a right triangle?

Back

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

Front

Does the set of numbers 20, 25, 15 represent a right triangle?

Back

Yes, because 20² + 15² = 400 + 225 = 625 = 25².

Front

Is the statement 'The Pythagorean Theorem is a² + b³ = c⁴' true or false?

Back

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

Front

What does it mean when we say 'all of the a square plus all of the b square will perfectly fill the c square'?

Back

It means that the area of the squares constructed on the two shorter sides (a and b) equals the area of the square constructed on the hypotenuse (c). This is a visual representation of the Pythagorean Theorem.

Front

Find the length of the missing side if one side is 5 cm and the hypotenuse is 13 cm.

Back

The missing side is 12 cm, calculated using the formula: 13² - 5² = 169 - 25 = 144, so √144 = 12.

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 hypotenuse.

Front

What is the term for side c in a right triangle?

Back

Hypotenuse.

Front

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

Back

The hypotenuse is 10 cm, calculated as: √(6² + 8²) = √(36 + 64) = √100 = 10.