Archive for the ‘Geometry’ Category

One of my students gave me a problem last fall that was very interesting.

The problem is posed with the following diagram:


What is the measure of \angle CDA?  That is, what is the value of x?

I’ve given a similar problem in my trigonometry class for the past few years, except that version of the problem has a side length included and the triangle is not isosceles.

A pdf of this problem is linked below:


Working from my experience with the other version of this problem, I began to write in values for the various unlabeled angles in the diagram – if we label the intersection of \overline{AD} and \overline{BC} as K, then \angle CKD and \angle AKB are both 70^{\circ}, \angle CKA and \angle DKB are both 110^{\circ}, which makes \angle KCA 50^{\circ} and \angle ADB is 40^{\circ}.

I added in new variables and created a system of four equations with four unknowns, but it was a dependent system.

The solution for this problem that was devised by the student who gave it to me is after the jump…


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