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