Geometry: An Interactive Journey to Mastery

Solutions

Lesson 1

1. False. A circle drawn on the surface of a donut, for example, need not
   GLYLGHWKHVXUIDFHLQWRWZRSDUWV௘6HHFigure S.1.1௘


2. There is no example of a perfectly straight line in the room you currently
   sit in. At the microscopic level, there are sure to be bumps and niches in anything you point out.
   ͼ௘,VQ¶WLWFXULRXVWKDWZHDOOKDYHSURJUDPPHGLQRXUPLQGVWKHFRQFHSWRIDSHUIHFWO\VWUDLJKWOLQH
   HYHQWKRXJKZHKDYHQHYHUVHHQRQH"௘ͽ


3. Like the scaling feature on smartphone maps, it seems that all shadows of straight objects are again straight
   ͼ௘LQDEURDGVHQVHSXWWLQJLVVXHVRI3UREOHPDVLGH௘ͽ,VLWDWDOOREYLRXVWKDWWKLVVKRXOGEHWKHFDVH"
   ͼ௘:H¶OOH[SORUHWKLVLQ/HVVRQ௘ͽ

Lesson 2

1. D௘ͽ 7UXH
   E௘ͽ )DOVH
   F௘ͽ 7UXHͼ௘DQ\WKUHHSRLQWVDUHFRSODQDU௘ͽ
   G௘ͽ 7UXH
   H௘ͽ 7UXH
   I௘ͽ 7UXH


2. D௘ͽ &RUUHFW
   E௘ͽ 1RWFRUUHFW,WVKRXOGUHDGAB#CD.
   F௘ͽ 1RWFRUUHFW,WVKRXOGUHDGAB = CD.
   G௘ͽ &RUUHFW

Figure S.1.1