Geometry Section 7-1D Golden Rectangles Page 478 You will need a calculator with sin/cos/tan in 1

1
Geometry Section 7-1D Golden RectanglesPage
478You will need a calculator with sin/cos/tan
in 1½ weeks.Freshmen - TI 30 XII S
recommended. Around 15. Youll need it for
Alg. II.
2
Golden Rectangles
Pg.478
Rectangle ACDF is a golden rectangle if and only
if square ABEF with side lengths W makes
rectangle CDEB similar to rectangle ACDF.
3
Golden Rectangles
If you cut a golden rectangle into a square and a
small rectangle, the small rectangle is also a
golden rectangle.
Pg.478
4
Golden Rectangles
All Golden Rectangles are similar.
If we calculate the ratio of the sides of all
Golden Rectangles, we would discover the Golden
Ratio.
Pg.479
The Golden Ratio 1.618 This is the ratio of the
long side short side.
Ratio of short side long side
0.618
5
Donald Duck in Mathamagic Land - 1959
6
Try It
HIJK is a golden rectangle. Use an approximation
for the golden ratio to find each length to the
nearest tenth.
Pg.479
a. If IJ 25, find JK.
25(1.618) 40.5
b. If HI 10, find HK.
10(.618) 6.2
7
Exercises
Identify the golden rectangle.
1 Pg.480
b
8
Exercises
GHIF is a golden rectangle. Find each ratio.
GH HI
GJ JI
1.618
.618
2-5 Pg.480
If GH 25, find HI to the nearest hundredth.
25(.618) 15.45
If GJ 100, find JI to the nearest hundredth.
100(1.618) 161.8
9
Exercises
Find the area of a golden rectangle whose width
is 20. Then find the length and width of a
golden rectangle that has twice that area.
If width 20, then length 20(1.618) 32.36
7 Pg.480
Area length x width
32.36(20) 647.2
A.R. 2
S.R. Ö2 1.41
Width 20(1.41) 28.2
Length 32.36(1.41) 45.63
10
Exercises
If you divide the length of a ______________by
its width, the number that you get is the
_____________.
If you divide the length of a golden rectangle by
its width, the number that you get is the golden
ratio.
8 Pg.480
11
Homework Practice 7-1DQuiz Tomorrow