Pythagorean Theorem leg hypotenuse A triangle is a right triangle if and only if the sum of the squares of the lengths of the legs equals the square of

Pythagorean Theorem

leg

leghypotenuse

A triangle is a right triangle if and only if the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

leg2 + leg2 = hypotenuse2

222 cba

ac

b

Pythagorean Theorem

Steps for solving a problem using the Pythagorean Theorem

1) Draw and label a diagram using the given values or information.

2) Write the Pythagorean theorem.

Let a and b represent the legs of a right triangle and c represent the hypotenuse. Find the unknown length.

10,4 ca

4

10b

222 cba

3) Substitute the given values into the equation.4) Solve for the unknown value. Simplify the square root, if needed. Leave exact values unless otherwise stated in the problem.

222 104 b10016 2 b842 b

84b

212b

5) If units are given in the problem, don’t forget them in your answer.

Example 1:

Pythagorean Theorem




Let a and b represent the legs of a right triangle and c represent the hypotenuse. Find the unknown length.

20,10 ba

10

c20

222 cba


222 2010 c2400100 c2500 c

c500

c510


Example 2:

Pythagorean TheoremLet a and b represent the legs of a right triangle and c represent the hypotenuse. Find the unknown length.

30,6 ba

Practice 1:

12,7 cb

Practice 2:

Pythagorean Theorem




60

c30

222 cba


222 6030 c23600900 c24500 c

c4500feet67c


Example 3:

A rectangular pool is 30 feet wide and 60 feet long. You swim diagonally across the pool. To the nearest foot, how far do you swim.

You swim about 67 feet across the pool.

Pythagorean TheoremPractice 3:

The diagonal of a rectangular wall measures 14 meters. One side of the wall is 10 meters long. What is the length of the other side?

Pythagorean Theorem

Example 4:

4, 5, 6

Tell whether the given side lengths is a right triangle.

If a triangle is a right triangle then it will satisfy the Pythagorean Theorem

If this is a right triangle, then the longest side would be hypotenuse, so let c = 6.

222 cba 222 654

362516 3641

This is not a right triangle.

Example 5:

8, 15, 17

222 cba 222 17158

28922564 289289

This is a right triangle.

Pythagorean Theorem

Practice 4:

9, 12, 15

Tell whether the given side lengths is a right triangle.

Practice 5:

7, 11, 13

Pythagorean TheoremExample 6:

A real estate lot is in the shape of a triangle. The side lengths are 48 feet, 55 feet, and 73 feet. The real estate agent told a potential buyer that one of the corners forms a right triangle. Is the real estate agent correct?


A window has the shape of a triangle with side lengths of 120 centimeters, 120 centimeters, and 180 centimeters. Is the window a right triangle? Explain.


Justin hikes 7 miles due east and then 3 miles due north. How far is he from his starting point?


Find the length of the diagonal of a rectangle whose length is 8 meters and width is 5 meters.


The playing bed of a shuffleboard table is in the shape of a rectangle. If the plying bed measures 154 inches by 20 inches, what is the length of the diagonal from one corner of the playing bed to the opposite corner? Round your answer to the nearest inch.


A baseball diamond is a square 90 feet on a side. What is the distance from first base to third base?

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Pythagorean Theorem leg hypotenuse A triangle is a right triangle if and only if the sum of the squares of the lengths of the legs equals the square of