1 Geometry Section 7-1D Golden Rectangles Page 478 You will need a calculator with sin/cos/tan in 1½ weeks. Freshmen - TI 30 XII S recommended. Around $15. You’ll need it for Alg. II.

2 Golden Rectangles: Rectangle ACDF is a golden rectangle if and only if square ABEF with side lengths W makes rectangle CDEB similar to rectangle ACDF. Pg. 478

3 Golden Rectangles: Pg. 478 If you cut a golden rectangle into a square and a small rectangle, the small rectangle is also a golden rectangle.

4 Golden Rectangles: Pg. 479 All Golden Rectangles are similar. If we calculate the ratio of the sides of all Golden Rectangles, we would discover the Golden Ratio. The Golden Ratio  This is the ratio of the long side: short side. Ratio of short side: long side  0.618

5 “Donald Duck in Mathamagic Land”

6 Try It: Pg. 479 HIJK is a golden rectangle. Use an approximation for the golden ratio to find each length to the nearest tenth. a. If IJ = 25, find JK. 25(1.618)  40.5 b. If HI = 10, find HK. 10(.618)  6.2

7 Exercises: #1 Pg. 480 Identify the golden rectangle. b

8 Exercises: 2-5 Pg. 480 GHIF is a golden rectangle. Find each ratio GH HI.618 GJ JI If GJ = 100, find JI to the nearest hundredth. 100(1.618) = If GH = 25, find HI to the nearest hundredth. 25(.618) = 15.45

9 Exercises: 7 Pg. 480 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. Area = length x width 32.36(20) = If width = 20, then length = 20(1.618) = A.R. = 2 S.R. =  2  1.41 Width = 20(1.41) = 28.2 Length = 32.36(1.41) = 45.63

10 Exercises: 8 Pg. 480 If you divide the length of a golden rectangle by its width, the number that you get is the golden ratio. If you divide the length of a ______________by its width, the number that you get is the _____________.

11 Homework: Practice 7-1D Quiz Tomorrow