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