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 a right triangle?

Back

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

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 side lengths 6, 6.7, and 3, which side is the hypotenuse?

Back

6.7

Front

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

Back

To find a missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

Find the missing side if one side is 6 and the hypotenuse is 6.4.

Back

The missing side is 6.4² - 6² = 6.4.

Front

What is the diagonal length of a rectangle with sides 9 in and 11 in?

Back

The diagonal length can be found using the Pythagorean Theorem: √(9² + 11²) = √(81 + 121) = √202 ≈ 14.2 in.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If one side of a right triangle is 8 and the hypotenuse is 10, what is the length of the other side?

Back

Using the Pythagorean Theorem: 10² - 8² = 100 - 64 = 36, so the other side is √36 = 6.

Front

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

Back

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