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 works on right triangles.

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the formula to find the length of the 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 10 and one side is 6, what is the length of the other side?

Back

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

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

Casey travels 12 miles west and 16 miles north. How far is she from her starting point?

Back

20 miles (Using the Pythagorean Theorem: 12² + 16² = 144 + 256 = 400; √400 = 20).

Front

What is a right triangle?

Back

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

Front

If a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

Back

13 (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What is the hypotenuse in a right triangle?

Back

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