median
don steward
mathematics teaching 10 ~ 16

Friday, 21 October 2016

circle theorems using parallels

normally the circle theorems are justified using isosceles triangles
but it's quite neat to use alternate and corresponding angles on parallel lines

this and other ideas are explored more substantially by Dietmar Kuchemann in this article

construct a parallel line



























but A = B



the angle in a semicircle being 90 degrees can follow from the fact that an isosceles triangle is perpendicularly bisected by its line of symmetry

construct a parallel line














 

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