1. Warm Up
You need to tie up a volleyball net with poles that are 10 feet off the ground. To meet safety code, the stakes must be 7 feet from the net and the rope used must be in one piece. You check the PE supply shed and find two lengths of rope, one 12 feet and the other 13 feet. Will you be able to tie up the net according to safety code?

2. Converse of The Pythagorean Theorem
Essential Question?
How can you test the converse of the Pythagorean Theorem and use it to solve problems?
8.G.6

3. Common Core Standard:
8.G ─ Understand and apply the Pythagorean Theorem.
6. Explain a proof of the Pythagorean Theorem and its converse.

4. Objectives:
To use the converse of the Pythagorean Theorem.

5. Conditional Statements
A CONDITIONAL STATEMENT is a statement that can be written in “if-then” form.
“If …, then …”
The hypothesis (premise) is the part of the statement that follows “if”.
The conclusion is the part of the statement that follows “then”.
hypothesis (premise)
conclusion

6. Conditional Statements
If a and b are real numbers, then a + b is a real number.
If you are in the choir, then you are a good singer.
You will pass this class, if you study and do well on tests.
hypothesis (premise)
conclusion
hypothesis (premise)
conclusion
conclusion
hypothesis (premise)

7. Curriculum Vocabulary
Converse (inverso):
A theorem whose hypothesis and conclusion are the conclusion and hypothesis of another.
Example:
STATEMENT: If a polygon is a triangle, then the sum of the interior angles of the polygon is 180°.
CONVERSE: If the sum of the interior angles of a polygon is 180°, then the polygon is a triangle.

8. The Pythagorean Theorem and Its Converse
The Pythagorean Theorem states that if a triangle is a right triangle (with legs 𝑎 & 𝑏 and hypotenuse 𝑐), then 𝑎 2 + 𝑏 2 = 𝑐 2 . The CONVERSE of the Pythagorean Theorem states that if 𝑎 2 + 𝑏 2 = 𝑐 2 , then the triangle is a right triangle.
Fill out the table and decide if the lengths would represent a right triangle:
Side 1
Side 2
Side 3
Does 𝒂 𝟐 + 𝒃 𝟐 = 𝒄 𝟐
Is this a right triangle? 3 4 5 12 13 7 24 25 17 8 15 20 29 21
How did you know which number to use for 𝑐 ?

9. The Converse of the Pythagorean Theorem
Decide if the given lengths represent a right triangle:
Side 1 = 9 inches Side 2 = 40 inches Side 3 = 41 inches

10. The Converse of the Pythagorean Theorem
Decide if the given lengths represent a right triangle:
Side 1 = 8 meters Side 2 = 10 meters Side 3 = 12 meters