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 c² = a² - b² true or false?

Back

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

Front

What is the length of the hypotenuse if one side is 5 cm and the other side is 12 cm?

Back

13 cm. Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, so c = √169 = 13.

Front

If the sides of a triangle are 15, 12, and 9, do they form a right triangle?

Back

Yes. To check, use the Pythagorean Theorem: 15² = 12² + 9², which simplifies to 225 = 144 + 81.

Front

What is the longest side of a right triangle called?

Back

The hypotenuse.

Front

In a right triangle, which side is always the longest?

Back

The hypotenuse is always the longest side.

Front

If a triangle has sides of lengths 8 cm, 15 cm, and 17 cm, does it form a right triangle?

Back

Yes. 17² = 8² + 15², which simplifies to 289 = 64 + 225.

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

If one side of a right triangle is 6 cm and the hypotenuse is 10 cm, what is the length of the other side?

Back

8 cm. Using the Pythagorean Theorem: b² = 10² - 6² = 100 - 36 = 64, so b = √64 = 8.

Front

What do you call a triangle with one right angle?

Back

A right triangle.