Wednesday, December 3, 2008
Geometry Problem Requiring Critical Reading & Thinking
Exactly two of the sides of a triangle are congruent and one of the equal angles is known to have degree measure greater than 50. How many integer values are possible for the measure of the remaining angle (the one that is different from the base angles)?
Comments:
(1) This is not intended to be a significant challenge. Rather it is meant as a warmup or for a slightly more extended discussion.
(2) Since middle school students know the sum of the angles of a triangle and can be told the basic fact about the base angles of an isosceles triangle, this problem is appropriate for them too.
(3) How would you expect most students to approach this? Do you think the majority would start by plugging in 51, 52, 53, etc.?
(4) Does this type of question promote important problem-solving skills and strategies? Do students recognize the significance of the 'boundary values' 50 and 90, values that are not in the domain of the base angles yet can be critical for the analysis?
(5) There are at least two 'traps' set in this problem that are intended to help students become more critical thinkers and not jump too quickly to conclusions. After all, what is a trap? If one is circumspect, details are not so easily overlooked.
Posted by Dave Marain at 2:39 PM 4 comments
Labels: geometry, inequalities, SAT-type problems, triangles