The Pythagorean Theorem Flashcard

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 works on right triangles.

Front

If one side of a right triangle is 12 and the other side is 16, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 12² + 16² = 144 + 256 = 400. Therefore, c = √400 = 20.

Front

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

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If the hypotenuse of a right triangle is 50 and one side is 30, what is the length of the other side?

Back

Using the Pythagorean Theorem: 50² = 30² + b². Therefore, 2500 = 900 + b², so b² = 1600, and b = √1600 = 40.

Front

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

Back

In a right triangle, the length of the hypotenuse is always greater than either of the other two sides.

Front

Can the Pythagorean Theorem be used for obtuse or acute triangles?

Back

No, the Pythagorean Theorem is specifically for right triangles.

Front

If a right triangle has sides of length 8 and 15, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17.

Front

What is the value of the hypotenuse if both legs of a right triangle are equal to 10?

Back

Using the Pythagorean Theorem: c² = 10² + 10² = 100 + 100 = 200. Therefore, c = √200 = 10√2 or approximately 14.1.

Front

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

Back

Using the Pythagorean Theorem: 13² = 5² + b². Therefore, 169 = 25 + b², so b² = 144, and b = √144 = 12.