8-4 similarity in right triangles · 2003. 4. 13. · theorem 8-3 altitude similarity theorem the...

7-4

Similarity in Right Triangles

One Key Term

One Theorem

Two Corollaries

Daily Learning Target (DLT)

Monday March 4, 2013 “I can understand, apply, and remember

how to find relationships in similar right

triangles.”

Assignment Pages 385-388 (1-17, 28, 45, 46, 48)

1. ∆ABC ~ ∆FED, sss 10. x = 7.5, aa

2. Not Enough Info.

3. - Possible for Example 1

- Not Possible For Example 2

4. ∆FHG ~ ∆KHJ, aa

5. Not Proportional

6. Not Proportional

7. ∆APJ ~ ∆ABC, sss or sas

8. ∆NPM ~ ∆NQR, sas

9. Not Proportional

Assignment Pages 385-388 (1-17, 28, 45, 46, 48)

11. x = 2.5, aa 46. J

12. x = 12-5/6, aa 48. 30 FT

13. x = 12, aa

14. x = 8, aa

15. x = 15, aa

16. x = 12 m, sas

17. x = 220 yds, aa

28. 45 ft

45. C

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

7.4 Assignment

Pages 394 (1-13 Odds, 15-22, 49-51)

Exit Quiz – 5 Points

1512

54

S

R T

P Q

Find the ratios (Scale Factor)

of the lengths of the

corresponding sides of the

large triangle over the small

triangle.