Problem: The 100 degree isosceles triangle
I have looked at this problem in several different ways and I do not have a solution thus far.
Given an isosceles triangle ABC with AB=AC and the measure of angle BAC=100 degrees. Extend AB to point D such that AD=BC. Now draw segment CD. What is the size of angle BCD?
Initially I constructed an equilateral triangle with side AD. I proceded to construct another triangle CFE. From my constructions I made the following observations Each angle measure is color coded in the figure below. Segments AD, DE, AE and BC are all congruent segments by construction. Also note that segment AF is congruent to segment FC. From this point I can not quite figure out what I need to do next, but I feel confident that in the future I will find a solution to this problem.
