1. Class Greeting

2. Objective: The students will solve problems using the Pythagorean Theorem.

3. The Pythagorean Theorem
Chapter 8 – Lesson 2
The Pythagorean Theorem

4. The Pythagorean Theorem
c2 = a2 + b2

5. The Converse of the Pythagorean Theorem
a2 + b2 = c2

6. The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths.

7. Example 1A: Using the Pythagorean Theorem
Find the value of x. Give your answer in simplest radical form.
a2 + b2 = c2
Converse of the Pythagorean Theorem
= x2
Substitute 2 for a, 6 for b, and x for c.
40 = x2
Simplify.
Find the positive square root.
Simplify the radical.

8. You can also use side lengths to classify a triangle as acute or obtuse.

9. To understand why the Pythagorean inequalities are true, consider ∆ABC.

10. By the Triangle Inequality Theorem, the sum of any two side lengths of a triangle is greater
than the third side length.
Remember!

11. Example 4A: Classifying Triangles
Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
5, 7, 10
Step 1 Determine if the measures form a triangle.
By the Triangle Inequality Theorem, 5, 7, and 10 can be the side lengths of a triangle.

12. Step 2 Classify the triangle.
Example 4A Continued
Step 2 Classify the triangle.
c2 = a2 + b2 ?
Compare c2 to a2 + b2.
102 = ?
Substitute the longest side for c.
100 = ?
Multiply.
100 > 74
Add and compare.
Since c2 > a2 + b2, the triangle is obtuse.

13. Example 4B: Classifying Triangles
Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
5, 8, 17
Step 1 Determine if the measures form a triangle.
Since = 13 and 13 > 17, these cannot be the side lengths of a triangle.

14. Check It Out! Example 4a
Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
7, 12, 16
Step 1 Determine if the measures form a triangle.
By the Triangle Inequality Theorem, 7, 12, and 16 can be the side lengths of a triangle.

15. Check It Out! Example 4a Continued
Step 2 Classify the triangle.
c2 = a2 + b2 ?
Compare c2 to a2 + b2.
162 = ?
Substitute the longest side for c.
256 = ?
Multiply.
256 > 193
Add and compare.
Since c2 > a2 + b2, the triangle is obtuse.

16. Check It Out! Example 4b
Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
11, 18, 34
Step 1 Determine if the measures form a triangle.
Since = 29 and 29 > 34, these cannot be the sides of a triangle.

17. Kahoot!

18. Lesson Summary:
Objective: The students will solve problems using the Pythagorean Theorem.

19. Preview of the Next Lesson:
Objective: The students will solve problems involving Special Right Triangles.

20. Stand Up Please