1. Warm Up Write down objective and homework in agenda
Lay out homework (Simplify Radicals)
Homework (Pythagorean Worksheet kuta)

2. Warm Up
The distance from Jonestown to Maryville is 180 miles, the distance from Maryville to Elm City is 300 miles, and the distance from Elm City to Jonestown is 240 miles. Do the three towns form a right triangle? Why or why not?
Solution: If these three towns form a right triangle, then 300 would be the hypotenuse since it is the greatest distance.
= 3002
= 90000
90000 =
These three towns form a right triangle.

3. Simplify the radicals

4. Vocabulary hypotenuse
longest side of a right triangle, opposite the right angle
legs
the two sides of a right triangle that make up the right angle
right angle
angle that measures 90 degrees
Pythagorean Theorem
theorem that states in a right triangle the length of the hypotenuse (c) squared is equal to the sum of the squares of the lengths of the legs a2 + b2 = c2
Pythagorean Triple
three positive integers that make up the lengths of the sides of a right triangle

5. Pythagorean Theorem Deals with the relationship between the side lengths in a right triangle
Sides A and B are called the….
Legs!
Side C is called the….
Hypotenuse
Side C is always the ….
Longest side!
Side C is always across the right angle

6. Pythagorean Theorem The formula for the Pythagorean Theorem is
a2 + b2 = c2

7. Example 1 Calculate the missing side of a right triangle
a2 + b2 = c2
= x2
= x2
549 = x2
x = 23.4 ft
hypotenuse
leg
leg

8. Example 2 Calculate the missing side of a right triangle
a2 + b2 = c2
82 + x2 = 122
64 + x2 = 144
x2 = 80
x = 8.9 cm
leg
leg
hypotenuse

9. Example 3
a2 + b2 = c2
x2 = 7.42
x2 = 54.76
x2 = 41.8
x = 64.5

10. You Try! Calculate the missing side of a right triangle
a2 + b2 = c2
x = 4.9
leg
leg
hypotenuse

11. You Try!
X = 5.4

12. Pythagorean Triple
A Pythagorean triple consists of three positive WHOLE NUMBER that fit into the Pythagorean Theorem
Example: = 52

13. Example 1 Determine whether a triangle with the given side lengths is a right triangle
7 in, 24 in, 25 in
(always place numbers in the order listed into the formula)
= 252
= 625
625 = 625
Yes, it is a right triangle

14. Example 2 Determine whether a triangle with the given side lengths is a right triangle
6 m, 7 m, Ѵ85m
(always place numbers in the order listed into the formula)
= Ѵ852
= Ѵ852
85 = Ѵ852
85=85
Yes, it is a right triangle

15. You Try! Determine whether a triangle with the given side lengths is a right triangle
8 cm, 10 cm, 12 cm
No, it is NOT a right triangle!
= 12.8

16. You Try! Determine whether a triangle with the given side lengths is a right triangle
a = 6.4, b = 12, c = 12.2
NO!

17. Find the circumference and area of the circle below:
First calculate r.
Side MP = 12 in.
= r2
r = 13 in.
C = 2πr
C = 2(3.14)(13)
C = 81.6 in.
A = πr2
A = (3.14)(132)
A = in2

18. Practice! http://www.quia.com/rr/624643.html

19. Extra Resources