Flashcards: 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 are the side lengths of a right triangle?

Back

The side lengths of a right triangle must satisfy the Pythagorean Theorem. For example, the lengths 6, 8, and 10 form a right triangle because 6² + 8² = 10² (36 + 64 = 100).

Front

How do you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

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

Back

In a right triangle, the longest side is called the hypotenuse, and it is opposite the right angle. The other two sides are called legs.

Front

If you know the hypotenuse and one leg, how do you find the missing leg?

Back

To find the missing leg, use the formula: missing leg = √(hypotenuse² - known leg²).

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) × base × height.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

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

Back

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

Front

What is the width of a rectangular parking lot with a diagonal of 60 meters and a length of 48 meters?

Back

The width can be found using the Pythagorean Theorem: width = √(60² - 48²) = √(3600 - 2304) = √1296 = 36 meters.

Front

What do you do if you need to find a missing leg in a right triangle?

Back

You subtract the square of the known leg from the square of the hypotenuse.