Guillermo, over at "Proofs from the Book," has recently posted an interesting discussion about the Midsegment Theorem, which deals with the line that connects the two midpoints of two sides of a triangle. This concept is useful when doing proofs with triangles. According to Guillermo, the midsegmet (or midline) has these properties:
"(1) the midsegment connecting the midpoints of the two sides of a triangle is parallel to the third side and (2) its length is also half of the third side."
If you learn how to recognize this geometrical identity, it will be very valuable to you when working with geometry or trigonometry questions. The post at that site goes into great detail to explain each step of the proof for each of these two theorems. It is fascinating to see the in-depth steps that go towards demonstrating a mathematical proof, so I recommend this page at http://proofsfromthebook.com/2013/03/25/the-midsegment-theorem/ for anyone interested in learning more about the midsegment theorem.