Pythagorean Theorem Flashcard

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle, typically referred to as sides 'a' and 'b'.

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

How do you identify the hypotenuse in a right triangle?

Back

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

Front

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

Back

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

Front

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

Back

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², depending on which side is missing.

Front

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

Back

Using the Pythagorean Theorem: b² = 13² - 5² = 169 - 25 = 144, so b = √144 = 12.

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 value of the hypotenuse if both legs of a right triangle are equal to 1?

Back

Using the Pythagorean Theorem: c² = 1² + 1² = 1 + 1 = 2, so c = √2.