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 can you determine if a set of numbers represents the sides of a right triangle?

Back

To determine if a set of numbers represents the sides of a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers.

Front

If a triangle has sides of lengths 20, 25, and 15, does it form a right triangle?

Back

Yes, because 20² + 15² = 400 + 225 = 625, which is equal to 25².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

Front

If one side of a right triangle is 12 cm and the other side is 16 cm, what is the length of the hypotenuse?

Back

The hypotenuse is 20 cm, calculated as √(12² + 16²) = √(144 + 256) = √400 = 20.

Front

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

Back

In a 3-4-5 triangle, the sides are in the ratio of 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²).

Front

How do you solve for a missing side in a right triangle?

Back

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

Front

If the hypotenuse is 10 cm and one side is 6 cm, how do you find the other side?

Back

Use the formula: b = √(c² - a²). Here, b = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

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

Back

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