1. Converse of the Pythagorean Theorem January 6, 2012

2. Entering Activity ∆Complete the objective test that you were given. ∆If you did not receive an objective test, then you will complete the logic problem that is on the next slide. ∆When you finish the objective test, you will work on the logic problem, that is on the next slide.

3. Agenda ∆Vocab Quiz ∆Sponge Quiz ∆Objective Tests ∆Discuss agenda ∆Converse of the Pythagorean Theorem ∆Exit Slip

4. Learning Targets ∆I can evaluate square roots of small perfect squares. ∆I can recall the Pythagorean Theorem. ∆I can explain a proof of the Pythagorean Theorem’s Converse.

5. Converse of the Pythagorean Theorem ∆Remember that the Pythagorean Theorem states, a 2 + b 2 = c 2 ∆We will use this to test and see if a set of numbers will create a right triangle. ∆The set of numbers used to create a right triangle are called Pythagorean Triples.

6. Converse of the Pythagorean Theorem ∆Example 1: 3, 4, 5 – Step 1: Start with the Pythagorean Theorem – Step 2: Replace a with 3 – Step 3: Replace b with 4 – Step 4: Replace c with 5 – Step 5: Evaluate the Squares – Step 6: Simplify – Step 7: Compare

7. Converse of the Pythagorean Theorem ∆Example 1: 3, 4, 5 – Step 1: a 2 + b 2 = c 2 – Step 2: 3 2 + b 2 = c 2 – Step 3: 3 2 + 4 2 = c 2 – Step 4: 3 2 + 4 2 = 5 2 – Step 5: 9 + 16 = 25 – Step 6: 25 = 25 – Step 7: Both sides are equal so yes, 3, 4 and 5 will make a right triangle.

8. Converse of the Pythagorean Theorem ∆Example 2: 5, 12, 13 – Step 1: a 2 + b 2 = c 2 – Step 2: 5 2 + b 2 = c 2 – Step 3: 5 2 + 12 2 = c 2 – Step 4: 5 2 + 12 2 = 13 2 – Step 5: 25 + 144 = 169 – Step 6: 169 = 169 – Step 7: Both sides are equal so yes, 5, 12 and 13 will make a right triangle.

9. Converse of the Pythagorean Theorem ∆Example 3: 15, 60, 61 – Step 1: a 2 + b 2 = c 2 – Step 2: 15 2 + b 2 = c 2 – Step 3: 15 2 + 60 2 = c 2 – Step 4: 15 2 + 60 2 = 61 2 – Step 5: 225 + 3600 = 3721 – Step 6: 3825 = 3721 – Step 7: Both sides are not equal so no, 15, 60 and 61 will not make a right triangle.

10. Converse of the Pythagorean Theorem ∆As a team, decide if the following numbers will create a right triangle: – On Your Own 1: 14, 48, 50 – On Your Own 2: 8, 13, 14

11. Exit Slip ∆Short Answer Practice – Remember Vocabulary Books are due tomorrow – Vocabulary Quiz Tomorrow – We will be taking notes after the quiz tomorrow

12. Homework ∆Complete a worksheet using the Converse of the Pythagorean Theorem to decide if a set of numbers will form a right triangle. – Numbers 3 and 5 are extra credit