Symmetry LinesDate: 03/30/2000 at 19:29:54 From: Ian Subject: Symmetry lines How many symmetry lines are in a circle? Date: 03/31/2000 at 18:13:58 From: Doctor Ian Subject: Re: Symmetry lines Hi Ian, I assume that you already understand that a line of symmetry is a line that divides a figure into two similar parts. Think about a circular clock. A line that goes through the 12 and the 6 cuts the clock into two similar pieces, so that's one line of symmetry. A line that goes through the 1 and the 7 is also a line of symmetry. Is there at least one other line of symmetry between those two lines? Yes, the one that goes through the point halfway between the 12 and the 1, and the point halfway between the 6 and the 7. Draw a picture and convince yourself that this is true. In fact, no matter how close together two lines of symmetry are, there will always be another one halfway between them. So if you ever _thought_ that you'd counted _all_ the lines of symmetry, there would always be at least one more that you hadn't counted yet. What does that tell you about the number of lines of symmetry in a circle? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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