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 hypotenuse 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 24 and the hypotenuse is 25, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + b² = c². Here, a = 24 and c = 25. So, b² = 25² - 24² = 625 - 576 = 49, thus b = 7.

Front

Do the lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

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

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

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

Back

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

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

A 3-4-5 triangle is a right triangle where the lengths of the sides are in the ratio 3:4:5, satisfying the Pythagorean Theorem.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Check if the square of the longest side equals the sum of the squares of the other two sides.

Front

What is the diagonal length of a rectangle with sides 9.2 in and 11 in?

Back

Use the Pythagorean Theorem: d² = 9.2² + 11². Thus, d = √(84.64 + 121) = √205.64 ≈ 14.35 in.

Front

What is the significance of the Pythagorean Theorem in real life?

Back

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