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7-4
Similarity in Right Triangles
One Key Term
One Theorem
Two Corollaries
Geometry Bell Ringer
x
4
9 y
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
Geometry Bell Ringer
x
4
9 y
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
4
y x
y 9
x 13
13
4 x
x
9
4 y
y
362 y522 x
6y132x
Daily Learning Target (DLT)
Monday March 11, 2013
“I can understand, apply, and remember how to find relationships in similar right triangles.”
Reminder: Because of the basketball game on Wednesday
March 13, 2013, thus canceling school, ALL
Term 3 work will be due tomorrow Tuesday
March 12, 2013 at 6 pm. So grades can be
posted ASAP.
7.4 Assignment Pages 394 (1-13 Odds, 15-22, 49-51)
1. 6 18. x =
3. 19. x = 12
5. 20. x = 60
7. 21. a. 18 Miles
9. s b. 24 Miles
11. c 22. KNL, JNK
13. h 49. x = 3
15. x = 9 50. x = 4
16. x = 20 51. x = 4.5
17. x = 10
34
214
66
36
7.4 Assignment Part 2 Pages 394-396 (26-36, 55-59)
26. 35. x =
27. 14 y = 12
28. 2 z =
29. 36. x = 4
30. 1 y =
31. 2.5 z =
32. 55. D 59.
33. 121 56. G a. Write Prop.
34. x = 12 57. C then cross
y = 58. H multiply
z = b.
34
14
512
1010
7374
56
132
133
133
Theorem 8-3
Altitude Similarity Theorem
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
CBDACDABC ~~
A
C
B D
Vocabulary
1. Geometric Mean 1.
b
x
x
a
abx
#1 Finding the Geometric Mean
Find the geometric mean of 15 and 20.
20
15 x
x
#2 Finding the Geometric Mean
Find the geometric mean of 15 and 20.
20
15 x
x
)20(15x
300x
310x
#2 Finding the Geometric Mean
Find the geometric mean of 10 and 7.
10
7 x
x
#2 Finding the Geometric Mean
Find the geometric mean of 7 and 10.
10
7 x
x
)10(7x
70x
70x
Corollary 1 to Theorem 8-3
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
DB
CD
CD
AD
A
C
B D
)(DBADCD
Corollary 2 to Theorem 8-3
The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.
,AB
AC
AC
AD
A
C
B D
AB
CB
CB
BD
#3
x
4
12 y
16
4 x
x
12
4 y
y
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
4 x
12 y
x 16
y
#3
x
4
12 y
16
4 x
x
12
4 y
y
642 x 482 y
8x 34y
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
4 x
12 y
x 16
y
#4
x
5
15 y
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
#4
y
5
15 x
20
5 y
y
x
x 15
5
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
5 y
15 x
y 20
x
1002 y 752 x
10y 35x
Expert Groups-Period 3
Group 1: Marco, Everett, Zack, Bradley
Group 2: Allison, Ajahnae, Sydney
Group 3: Andy, Robert, Cody, Colton
Group 4: Nicole, Samantha, Daniel, Drew
Expert Groups-Period 5
Group 1: Alissa, April, Cassaundra, Megan
Group 2: Cody, Jacob, Humberto, Matt
Group 3: Brandi, Geneva, Garrett, Keiton
Group 4: Kayla, Torie, Chris, Bruce
Expert Groups-Period 6
Group 1: Sarah, Bailey, Destiny, Hunter
Group 2: Spencer, Corey, Jody,
Group 2: Mark, Irisbel, Billy
Group 4: MJ, Alexes, Shyann
Expert Groups-Period 7
Group 1: Madison, Madison, Sierra, Shawlin
Group 2: Hannah, Destiny, Mc Kalyn, Ryan
Group 2: Brennix, Dustin, Alex
Group 4: Zack, Jacob, Michael
Geometry Closer
y
3
9 x
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
Geometry Bell Ringer
y
3
9 x
• Solve for x and y.
Small
Medium
Large
Leg Small Leg Large Hypotenuse
3
x y
x 9
x 12
9
3 x
x
12
3 y
y
362 y272 x
6y33x