The Pythagorean Theorem

Chapter 9.1

Part 2

The Converse of the Pythagorean Theorem:In a triangle with sides a, b, and c; if

,

then the triangle is a right triangle.

2 2 2a b c

Are the following right triangles?1. a = 9, b = 12, c = 15

2 2 2a b c 2 2 29 12 15

81 144 225 225 225

2. a = 1, b = 2, c = 3

True. Yes it is a right triangle.

2 2 2a b c 2 2 21 2 3 1 4 9

5 9False. Not a right triangle.

In your Notebooks:Is this a right triangle?

SHOW YOUR WORK!

1) 4, 5, 6 2) 8, 15, 17

3) 20, 21, 29 4) 3, 8, 15

We will continue taking notes in 5-10 minutes.

Word Problems:Suppose that you drive 4 miles south and then

10 miles east. How far are you away from your starting point?

Step 1: Draw a picture:

4 miles

10 miles

Word Problems:Suppose that you drive 4 miles south and then

10 miles east. How far are you away from your starting point?

Step 2: Set up and equation, and solve.

4 miles

10 miles

Distance from starting point

2 2 2a b c 2 2 24 10 c

216 100 c 2116 c 116 10.8c miles

Applications of the Pythagorean Theorem: Use your own paper.

• You may work in groups of 2-3.

• Passing the AIMS: pg 253, 1-4 all

• Create your own word problem using distances, and solve using the Pythagorean theorem. – For example: Bob walked 6 miles north, turned

and walked 8 miles west. How far away is he from his original position? Keep your papers

Pythagorean Triples: All three sides of a right triangle are positive integers.

Which of the following are Pythagorean triples. Justify your answers (use converse of Pythagorean Theorem.)

1) 30 , 40 , 50 2) 14, 48, 50

3) 12, 35, 37 4) 48, 55, 73

5) 36, 77, 85 6) 16, 30, 34

7) 9, 40, 41 8) 11, 60, 61

9) What do the following triples have in common? 10) Which ones are the sides of a right triangle?3, 4, 5

6, 8, 10

9, 12, 15

12, 16, 20

15, 20, 25

30, 40, 50

Hint: look for GCF and Factor

Homework: pg 417 (18, 21-32 all, 37)

For Converse of Pythagorean Theorem: EXPLAIN YOUR ANSWERS