median
don steward
mathematics teaching 10 ~ 16

Thursday 23 October 2014

angles in a triangle

three ways to justify that the angles in a triangle sum to 180 degrees

a ppt is here


1. a sequence,

  • starting with an isosceles right angled triangle (maybe with reference to this being half a square)
  • a right angled triangle (being half a rectangle)
  • an isosceles triangle (using two of (ii))
  • an acute angled triangle (also using two of (ii) but different triangles)
  • an obtuse angled triangle (made up with two right angled triangles)























(2) folding a triangle and involving reflection

























(3) the usual proof
create a line parallel to the base, through the apex
then involve angles on parallel lines (alternate angles) which can be justified by rotation


this is maybe more evident on a tessellation of triangles

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