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: 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 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

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

Front

What are the side lengths of a right triangle if the hypotenuse is 10 cm and one side is 6 cm?

Back

8 cm (using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, thus b² = 64, and b = √64 = 8).

Front

Can a triangle with sides 5, 12, and 13 be a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

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 equals the square of the longest side (hypotenuse).

Front

If a triangle has sides of lengths 8 cm, 15 cm, and 17 cm, is it a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289, which equals 17².

Front

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

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

What is a right triangle?

Back

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

Front

What are the possible side lengths of a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.