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

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

In a right triangle, if a = 3 and c = 5, what is b?

Back

Using the Pythagorean Theorem: c² = a² + b². So, 5² = 3² + b². This gives us 25 = 9 + b², thus b² = 16, and b = 4.

Front

What do you do to find the length of the hypotenuse in a right triangle?

Back

You add the squares of the lengths of the two other sides and then take the square root of that sum.

Front

If a right triangle has sides of length 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225. Therefore, c = √225 = 15.

Front

True or False: You ADD a² and b² then take the square root to find c on a right triangle.

Back

True.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

If the hypotenuse of a right triangle is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: c² = a² + b². So, 13² = 5² + b². This gives us 169 = 25 + b², thus b² = 144, and b = 12.

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.