Geometry: An Interactive Journey to Mastery

(Greg DeLong) #1

Solutions



  1. Draw a chord across part of the arc, and construct a perpendicular bisector of the chord. Do the same for a
    VHFRQGFKRUG7KHLQWHUVHFWLRQSRLQWRIWKHVHWZRSHUSHQGLFXODUELVHFWRUVLVWKHFHQWHURIWKHFLUFOHͼ௘&DQ
    \RXH[SODLQZK\WKLVLVWKHFDVH"௘ͽ
    Comment: If you rip the page from the book and hold it up to the light, you can fold a section of the arc
    onto itself. The crease is a perpendicular bisector of a chord. Do this again. Where the two creases intersect
    is the center of the circle.

  2. Yes. We have seen that if a and b have been constructed, then it is possible to construct a + b and also a.
    :HKDYHVHHQWKDWLVLWSRVVLEOHWRFRQVWUXFWDVHJPHQWRIDQ\ZKROHQXPEHUOHQJWK
    So, use the following steps to construct 123.
     )LUVWFRQVWUXFWVHJPHQWVRIOHQJWKVDQGͼ௘IURPDJLYHQVHJPHQWRIOHQJWK௘ͽ
    Next, construct a segment of length 3.
    Next, construct a segment of length 23.
    Next, construct a segment of length 23.
    Next, construct a segment of length 123.
    Finally, construct a segment of length 123.
    Lesson 27

  3. Verify that it does.

  4. In each case, they do.

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