1. Pythagorean Theorem
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.
hypotenuse
leg
leg
leg2 + leg2 = hypotenuse2
Discuss the parts of a right triangle, including where the legs and hypotenuse are located.

2. Pythagorean Theorem
Let a and b represent the legs of a right triangle and c represent the hypotenuse.
Find the unknown length.
Example 1:
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.
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.
5) If units are given in the problem, don’t forget them in your answer.

3. Pythagorean Theorem
Let a and b represent the legs of a right triangle and c represent the hypotenuse.
Find the unknown length.
Example 2:
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.
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.
5) If units are given in the problem, don’t forget them in your answer.

4. Pythagorean Theorem
Let a and b represent the legs of a right triangle and c represent the hypotenuse.
Find the unknown length.
Practice 2:
Practice 1:

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

6. Pythagorean Theorem Practice 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?

7. Pythagorean Theorem
Tell whether the given side lengths is a right triangle.
Example 4:
Example 5:
4, 5, 6
8, 15, 17
This is not a right triangle.
This 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.

8. Pythagorean Theorem
Tell whether the given side lengths is a right triangle.
Practice 4:
Practice 5:
9, 12, 15
7, 11, 13

9. Pythagorean Theorem Example 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?

10. Pythagorean Theorem Practice 6:
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.

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

12. Pythagorean Theorem Practice 7:
Find the length of the diagonal of a rectangle whose length is 8 meters and width is 5 meters.

13. Pythagorean Theorem Example 8:
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.

14. Pythagorean Theorem Practice 8:
A baseball diamond is a square 90 feet on a side. What is the distance from first base to third base?