AA ==BB

SECTION 7-SECTION 7-11

Jim Smith JCHSJim Smith JCHS

The Geometric Mean BetweenThe Geometric Mean Between2 Numbers ( A and B ), Is The2 Numbers ( A and B ), Is The

Number That When SubstitutedNumber That When SubstitutedFor X Will Make This ProportionFor X Will Make This Proportion

TrueTrue

AAXX== XXBB

Find the geometric meanFind the geometric mean between 4 and 9between 4 and 9

44XX

== XX99

X² = 36X² = 36 X² = 36X² = 36 X = 6X = 6

Find the geometric meanFind the geometric meanbetween 3 and 15between 3 and 15

33XX

== XX1515

X² = 45X² = 45 X² = 45X² = 45 X = 3 5X = 3 5 X = 6.7X = 6.7

8 is the geometric mean between8 is the geometric mean between2 and what number2 and what number

2288

== 88XX

2X = 642X = 64

X = 32X = 32

A

B

The Altitude Drawn To The The Altitude Drawn To The Hypotenuse In A Right Triangle Hypotenuse In A Right Triangle Divides The Hypotenuse Into 2 Divides The Hypotenuse Into 2

Parts. The Altitude Is The Geometric Parts. The Altitude Is The Geometric Mean Between The 2 Parts. Mean Between The 2 Parts.

AltAlt

AAAltAlt

== AltAlt BB

8

5XX

88XX

== XX55

X² = 40X² = 40 X = 40X = 40 X = 2 10X = 2 10 X = 6.3X = 6.3 Find XFind X

Each Leg Is The GeometricEach Leg Is The GeometricMean Between The Mean Between The PartPart Of The Of The

Hypotenuse Adjacent To The Leg Hypotenuse Adjacent To The Leg And The And The WholeWhole Hypotenuse Hypotenuse

Y

ZWW

XX

YYWW

== WWYY++ZZ

ZZXX

XXYY++ZZ

==

8

5

RR

TT

88TT

== TT8+58+5

T² = 8 ( 13 )T² = 8 ( 13 )T² = 104T² = 104 T = 104T = 104 T = 2 26T = 2 26 T = 10.2T = 10.2

Find TFind T

8

5

RR

TT

55RR

== RR5+85+8

R² = 5 ( 5+8 )R² = 5 ( 5+8 )R² = 5 (13 )R² = 5 (13 )R² = 65R² = 65 R = 65R = 65 R = 8.1R = 8.1Find RFind R