12.8 Pythagorean Review

Front

Do the segment lengths 15, 12, and 9 form a right triangle?

Back

Yes, because 15^2 = 12^2 + 9^2 (225 = 144 + 81).

Front

Find the length of the missing side if one side is 5 cm and the hypotenuse is 13 cm.

Back

12 cm, using the Pythagorean theorem: a^2 + b^2 = c^2.

Front

a=3, b=6, and c=9. Is this a right triangle?

Back

No, because 9^2 ≠ 3^2 + 6^2 (81 ≠ 9).

Front

Find the length of the missing side if one side is 60 in. and the hypotenuse is 80 in.

Back

80 in., using the Pythagorean theorem.

Front

What do we call the side across from the right angle?

Back

Hypotenuse.

Front

What is the Pythagorean theorem?

Back

a^2 + b^2 = c^2, where c is the hypotenuse.

Front

If one leg of a right triangle is 8 and the other leg is 15, what is the length of the hypotenuse?

Back

17, because 8^2 + 15^2 = 17^2.

Front

Can a triangle with sides 7, 24, and 25 be a right triangle?

Back

Yes, because 25^2 = 7^2 + 24^2 (625 = 49 + 576).

Front

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

Back

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

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

Back

8, using the Pythagorean theorem: 10^2 - 6^2 = b^2.