While listening to music, I noticed that the logo on my headphones is an example of two similar triangles. To prove this, I traced both triangles, and then found the midpoints of lines AC and BC. These two points happened to land precisely where expected, and so I connected them to form a white overlay of the symbol.
I used the measuring tool in GSP to find all five angles, which are listed on the left. By using the AA postulate, we can see that triangle ABC and triangle EDC are indeed similar.
Although it's not included in the picture above, I also measured angle AED. The sum of angles AED and BAC was 180 degrees, which proves that side AB is parallel to side ED.
(~GC2)
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