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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

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, so c = √100 = 10.

Front

Which set of sides can form a right triangle? 3, 4, 5 or 5, 5, 5?

Back

3, 4, 5 can form a right triangle because 3² + 4² = 5².

Front

What is the length of the missing side if the hypotenuse is 13 and one side is 5?

Back

Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12.

Front

True or False: The Pythagorean Theorem can be used for any triangle.

Back

False. The Pythagorean Theorem only works for right triangles.

Front

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

Back

The formula is a² + b² = c², where c is the hypotenuse.

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, so c = √225 = 15.

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

If the hypotenuse is 10 and one side is 6, what is the length of the other side?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8.