1. Agenda 1) Bell Work 2) Outcomes 3) Review/Finish 8.6 Notes
4) Pythagorean Theorem Geometry Pad activity
5) Pythagorean Theorem Notes
6) Exit Quiz
7) IP

2. Bell Work 2/11/13 1) Are the triangle similar?
2) Find the value of the variable
a) b)
3) Find the value of the variable

3. Outcomes I will be able to:
1) Solve for a missing length using a proportion
2) Use and understand triangle proportionality theorems
3) Use the Pythagorean Theorem to determine side lengths in a right triangle

4. Theorem 8.6
Theorem 8.6: If three parallel lines intersect two transversals, then they divide the transversals proportionally.
Meaning:

5. Examples
2.4
1.4
2.2 y x z
2.2

6. On Your OWN Find the value of x How do we set this up? 36 = 12x – 60

7. Theorem 8.7
Theorem 8.7: If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other to sides
Meaning:

8. Example
How do we set this up?
14 - x x

9. On Your OWN
Solve for p

10. Why does Pythagorean Theorem Work?
Log into class(password: Pythagoras)
Open Geometry Pad on your tablet.
Plot the points to make the 3 squares(ABCD, EFGH, IJKL)
Answer the questions
Draw a conclusion about why Pythagorean Theorem works

11. Results

12. Results

13. Pythagorean Theorem What is Pythagorean Theorem? a² + b² = c² c a
Pythagorean Theorem only works in what type of triangle?
***A right triangle c a b

14. Pythagorean Theorem
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.
We know: a² + b² = c²
Example:
How do we find x?
3² + 4² = x²
= x²
25 = x²
5 = x x 3 4

15. Pythagorean Theorem Example 2
1) Determine which pieces are: a, b, and c
a = 13 b = x c = 15
2) Plug into Pythagorean Theorem and solve
13² + x² = 15²
x² = 56
3) If not a perfect square, create a factor tree
to simplify
So,
***see board for work

16. Proof #2 9.2 Notes from Friday
Looking at
just the big square:
(a + b)(a + b)
Looking at little square
and 4 triangles:
c² + 4 x (1/2)(a x b)
(a + b)(a + b) = c² + 4 x (1/2)(a x b)
Use FOIL: a² + 2ab + b² = c² + 2ab
-2ab ab
a² + b² = c²

17. Pythagorean Triples
Pythagorean Triple: A set of three positive integers a, b, and c that satisfy the equation:
a² + b² = c²
For example: 3, 4, 5 are a Pythagorean Triple because:
3² + 4² = 5²

18. Pythagorean Triples
Examples: Show that the following are Pythagorean Triples
1. 6, 8, 10
2. 12, 16, 20
3. 5, 12, 13
4. 10, 24, 26
What pattern do you notice?
1 and 2 are multiples of 3, 4, 5 and 4 is a multiple of 3.
Note: If you multiply any set of Pythagorean triples by the same factor, then that set is also
a Pythagorean Triple.

19. Examples Try these without plugging into Pythagorean Theorem.
Just use the Pythagorean Triples we just discussed.

20. Finding Area
***You may need to use Pythagorean Theorem when finding the area of a triangle if the base or the height are missing.
Separate the triangles into two right triangles
if need be to find the length of the base.