Pythagorean Theorem Homework Assignment

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 is a Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c². Examples include (3, 4, 5) and (5, 12, 13).

Front

Does the set of numbers 15, 20, 25 represent a Pythagorean Triple?

Back

Yes, because 15² + 20² = 225 + 400 = 625 = 25².

Front

Find the length of the missing side if one side is 20 cm and the hypotenuse is 25 cm.

Back

The missing side is 15 cm, calculated using the Pythagorean Theorem: 20² + b² = 25², so b = 15.

Front

Find the length of the missing side if one side is 13 cm and the hypotenuse is 15 cm.

Back

The missing side is 8 cm, calculated using the Pythagorean Theorem: 13² + b² = 15², so b = 8.

Front

Does the set of numbers 4, 5, 6 represent a Pythagorean Triple?

Back

No, because 4² + 5² = 16 + 25 = 41, which is not equal to 6².

Front

Find the length of the missing side if one side is 48 in. and the hypotenuse is 52 in.

Back

The missing side is 20 in., calculated using the Pythagorean Theorem: 48² + b² = 52², so b = 20.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

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

Back

The hypotenuse is 20 cm, calculated using the Pythagorean Theorem: 12² + 16² = 144 + 256 = 400, so c = 20.

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 and a and b are the other two sides.