8-4 Similarity in Right Triangles - Montgomery County Schools · 7-4 Similarity in Right Triangles...

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