I was helping my sophomore friend with her geometry homework and came to problem 13a:
My first instinct was to use similar triangles and say $\triangle BKC \sim \triangle CMD$, and from there we can easily find the sidelengths.
However, in the class they have not learned triangle similarity (nor trigonometry), so they are not allowed to use it to solve problems.
What they have learned are triangle congruency (SSS, SAS, etc.), vertical angles, parallel lines with transversals (alternate interior angles, etc.), and Pythagoras' theorem. How would one solve this problem only using this knowledge? I'm at a loss.