Friday, August 15, 2014
Not quite back to school for most but the problem above might prove interesting to review some geometric/deductive reasoning.
For new geometry students, replace 'a' by a value, say 40, and ask them to fill in all the missing angles. Most should deduce that angle 5 = 50, but my educated guess is that many will assume b = 40, so
angle 5= angle 6 = 50 and angle 3 = angle 4 = 40. From there to angle 1 = angle 2 = 50, so
angle 2 + angle 3 = 90. QED! Not quite...
Well, the '90' is correct but the reasoning is another story! So this is all about justifying, checking validity of mathematical arguments, sorta' like some of the Eight Mathematical Practices of the Common Core!
In fact, you might ask them to redraw the diagram, keeping the given conditions but making it clear that b does not have to be 40 and that Angles 3&4 also do not have to be 40!