Understanding the 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 is expressed as a² + b² = c².

Front

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

Back

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

Front

If one side of a right triangle is 9 and the other side is 40, what is the length of the hypotenuse?

Back

c = √(9² + 40²) = √(81 + 1600) = √1681 = 41.

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 (legs) equals the square of the longest side (hypotenuse).

Front

Is the statement a² + b³ = c⁴ true or false?

Back

False. The correct statement is a² + b² = c².

Front

If a right triangle has legs of lengths 20 and 21, what is the length of the hypotenuse?

Back

c = √(20² + 21²) = √(400 + 441) = √841 = 29.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is given by d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

How can the Pythagorean Theorem be applied in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the shortest distance between two points, construction, navigation, and in various fields of engineering.

Front

What are the conditions for using the Pythagorean Theorem?

Back

The Pythagorean Theorem can only be used in right triangles, where one angle measures 90 degrees.

Front

If a right triangle has a hypotenuse of 50 and one leg of 30, what is the length of the other leg?

Back

b = √(50² - 30²) = √(2500 - 900) = √1600 = 40.