Pythagorean Theorem (Finding the Hypotenuse)

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 for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse (c) is: c = √(a² + b²).

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Front

What is the length of the hypotenuse if the two other sides are 5 cm and 12 cm?

Back

c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Front

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

Back

Use the formula: a² + b² = c². Here, b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is a right triangle?

Back

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

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

In the equation a² + b² = c², what do a and b represent?

Back

In the equation, a and b represent the lengths of the two legs of the right triangle.

Front

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

Back

The relationship is defined by the Pythagorean Theorem, which states that the sum of the squares of the legs equals the square of the hypotenuse.

Front

If a triangle has sides of lengths 8 cm and 15 cm, can it be a right triangle?

Back

To check, calculate: 8² + 15² = 64 + 225 = 289. The hypotenuse would be √289 = 17 cm, so yes, it can be a right triangle.