a nswers t o h omework 1) 3√152) 3√103) 6√64) 10√3 5) 4√56) 2√307) 5√78) 10√2 9)...
TRANSCRIPT
ANSWERS TO HOMEWORK
1) 3√152) 3√10 3) 6√6 4) 10√3
5) 4√5 6) 2√30 7) 5√7 8) 10√2
9) 6√5 10) 5√3 11) 12√3 12) 6√2
13) 15√2 14) 2√3 15) 2√6 16) 5√2 2
17) 2√218) 2√3 19) 8 20) 5√6
8-1 SIMILARITY IN RIGHT TRIANGLESAnswers to Warm Ups
1.
2.
3.
4.
5.
5 2
21 7
12 210
23
9
GEOMETRIC MEAN
Find the geometric mean of 2 and 3Remember a:b=c:d where b and c are the
means
2
3
x
x
2 6x
6x GeometricMean
a c
b d
TOO
Find the geometric mean of:
1) 2 and 6 2) 4 and 25*Remember what we learned yesterday!
2√3 10
SIMILAR TRIANGLESX
W
ZY
X
Y Z
X
Y
W
W
Y Z
∆XWY
∆XYZ
∆YWZ
∆XYZ ~ ∆XWY ~ ∆YWZX
W
ZY
X
Y Z
X
Y
W
W
Y Za
aa
b
b
b
c
c
d
d
e
e
e
d + c
d
ee
cAltitude (e) is geometric mean of pieces of hypotenuse (d,c)
∆XYZ ~ ∆XWY ~ ∆YWZX
W
ZY
X
Y Z
X
Y
W
W
Y Za
aa
b
b
b
c
c
d
d
e
e
e
d + c
d
a
a
d c
Legs (a,b) are geometric mean of hypotenuse (d+c) and adjacent piece (c,d)
c
b
b
d c
EXAMPLE
w is the geometric mean of g is the geometric mean of c is the geometric mean of
52
c
wg
2 and 52 and 7
5 and 7
2
5
w
w
2
7
g
g
5
7
c
c
TRY ON OWN
Which of these are geometric means? 2,b,c
Write out proportions and solve.
4a
c
2b
2
2 4
a
4
a b
b a
4
4
c
c a
a = 1
c = 2√5b = √5
TRY ON OWN
Which of these are geometric means? 9,z
Write out proportions and solve.
yx
15
z9
9
9 15
x 15x y
x z
z y
x = 5.4
z = 7.2
y = 9.6
HOMEWORK
Page 288 #1-39 odd