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

What does 'hypotenuse' refer to in a right triangle?

Back

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

Front

If one leg of a right triangle is 6 inches and the other leg is 8 inches, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10 inches.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two legs (a and b) equals the square of the hypotenuse (c): a² + b² = c².

Front

Is it necessary to label the sides of a right triangle as 'a' and 'b' in a specific order?

Back

No, it does not matter which leg is labeled as 'a' or 'b'; the theorem will still hold true.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: c² = a² + b². If c is known, use c² - b² = a² to find a, or c² - a² = b² to find b.

Front

If the hypotenuse of a right triangle is 13 inches and one leg is 5 inches, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 13² = 5² + b². Therefore, 169 = 25 + b², so b² = 144, and b = √144 = 12 inches.

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse states that if a triangle has sides a, b, and c, and a² + b² = c², then the triangle is a right triangle.