Pythagorean Theorem

Pythagorean Theorem Review

Pythagorean Theorem Basics

Hypotenuse

The hypotenuse of a right triangle is the largest side of the right triangle, and is always located across from the right angle.
The letter c is used to represent the hypotenuse.

Pythagorean Theorem Basics

Legs

The legs of a right triangle are the two shorter sides of the right triangle, and together form the right angle.
The letters a and b are used to represent the legs of the right triangle.

In the diagram to the right, the right triangle has side lengths of 3, 4 and 5.

​The sum of the squares of the two legs is equal to the square of the hypotenuse.

Pythagorean Theorem

The three sides of any right triangle will make the pythagorean true.
Therefore we can use the pythagorean theorem to determine whether 3 side lengths will make a right triangle.

Pythagorean Theorem

Multiple Choice

Determine which set of side lengths below form a right triangle.

• $$6,\ 9,\ 12$$

• $$10,\ 24,\ 26$$

Multiple Choice

Determine which set of side lengths below form a right triangle.

• $$20,\ 21,\ 29$$

• $$8,\ 13,\ 16$$

Multiple Choice

Determine which set of side lengths below form a right triangle.

• $$2.4,\ 4.5,\ 5.1$$

• $$3.2,\ 5.1,\ 7.3$$

Multiple Choice

Determine which set of side lengths below form a right triangle.

• $$5.2,\ 8.4,\ 10.5$$

• $$4.8,\ 5.5,\ 7.3$$

The Pythagorean Theorem can be used to determine the length of a missing side of a right triangle.

Finding the Hypotenuse

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 20.8

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 23.8

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 17

Deg^°

Rad

The Pythagorean Theorem can be used to determine the length of a missing side of a right triangle.

Finding a Leg

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 15.1

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 35

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 22.4

Deg^°

Rad

Multiple Select

Which set(s) of sides will form a right triangle? Choose all that apply.

• $$3,4,5$$

• $$10,\ 12,\ 14$$

• $$15,\ 20,\ 25$$

• $$8,\ 15,\ 17$$

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle shown. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 24.2

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle shown. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 23.4

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle shown. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 10.2

Deg^°

Rad

Math Response

Use the Pythagorean Theorem to determine the length of the missing side in the right triangle shown. Round your answer to the nearest tenth if necessary.

Type answer here

Correct Answer: 19.1

Deg^°

Rad