2. Remember Rough Draft is due Quiz Corrections are due
Make sure that you have your stuff
Calculator
Sharpened Pencil
Ruler
Protractor

3. Chapter 9 Right Triangles and Trigonometry
Section 9.2
Pythagorean Theorem
PROVE THE PYTHAGOREAN THEOREM
USE THE PYTHAGOREAN THEOREM

5. The Pythagorean Theorem
In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.

6. PROVING THE PYTHAGOREAN THEOREM
THEOREM 9.4 Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. b a c
c 2 = a 2 + b 2

7. USE THE PYTHAGOREAN THEOREM
True
True
False
False
True
True

8. Pythagorean Triples
If the sides of a Right triangle are integers, then the sides are known as a Pythagorean Triple
7, 24, 25
Do you know any other ?

9. USING THE PYTHAGOREAN THEOREM
A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation c 2 = a 2 + b 2. For example, the integers 3, 4, and 5 form a Pythagorean triple because 5 2 =

10. (hypotenuse)2 = (leg)2 + (leg)2
Finding the Length of a Hypotenuse 12 x 5
Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean triple.
SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2
Pythagorean Theorem
x 2 =
Substitute.
x 2 =
Multiply.
x 2 = 169
Add.
x = 13
Find the positive square root.
Because the side lengths 5, 12, and 13 are integers, they form a Pythagorean triple.

11. (hypotenuse)2 = (leg)2 + (leg)2
Finding the Length of a Leg
Many right triangles have side lengths that do not form a Pythagorean triple. x 14 7
Find the length of the leg of the right triangle.
SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2
Pythagorean Theorem
14 2 = x 2
Substitute.
196 = 49 + x 2
Multiply.
147 = x 2
Subtract 49 from each side.
147 = x
Find the positive square root.
49 • = x
Use product property.
= x
Simplify the radical.

12. Yes 5, 12, 13 is a Pythagorean triple
Finding the Missing Length
SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2
Pythagorean Theorem
13 2 = x 2
Substitute.
169 = x 2
Multiply.
25 = x 2
Subtract 144 from each side.
25 = x
Find the positive square root.
5= x
Simplify the radical.
Yes 5, 12, 13 is a Pythagorean triple

13. Area and the Right Triangle
Area equals ½ altitude times base A=½ab
b and a are the same as the legs of a Right triangle.

14. 2 poles are supported by 100ft cables 50 ft from the ground
How far are the poles apart?

16. Indirect Measurement
Closure Question
SUPPORT BEAM These skyscrapers are connected
by a skywalk with support beams. You can use the Pythagorean Theorem to find the approximate length of each support beam.

17. Closure Question x 2 = (23.26)2 + (47.57)2 x = (23.26)2 + (47.57)2
Indirect Measurement
Closure Question
23.26 m
47.57 m x
support
beams
Each support beam forms the hypotenuse of a right triangle. The right triangles are congruent, so the support beams are the same length.
x 2 = (23.26)2 + (47.57)2
Pythagorean Theorem
x = (23.26)2 + (47.57)2
Find the positive square root.
x  52.95
Use a calculator to approximate.
The length of each support beam is about meters.

18. HW Multi-Step Pythagorean Theorem Handout