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: c² = a² + b².

Front

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

Back

The formula to find the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

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

The hypotenuse is 5 cm, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What do you do when finding a missing side of a right triangle?

Back

You apply the Pythagorean Theorem: c² = a² + b², and rearrange the formula to solve for the missing side.

Front

In a right triangle, 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 a right triangle?

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If a² + b² = c² holds true for the lengths of the sides, then the triangle is a right triangle.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.