This week in Geometry we wrapped up a lot of material in one big chapter test. Now that we've finished studying relationships within triangles, I think we are moving on to quadrilaterals.
One of the relationships in triangles that we learned about this chapter is lines in triangles and their concurrent points. A concurrent point is a single point at which the lines intersect. In this case, the lines we learned about were medians, perpendicular bisectors, angle bisectors, altitudes and mid-segments; so the concurrent points we learned about were centroids, circumcenters, incenters, and othocenters respectively. It was really hard to remember which concurrent point went with which line, and what the special properties of each concurrent point was. Am example of one such property is a centroid is the center of gravity of the triangle. While studying these lines we also learned about coordinate proofs, so we could prove some theorems about the lines such as the Triangle Mid-segment Theorem.
As I mentioned in my previous blog, we also learned about indirect reasoning this chapter, which is proving a statement is right by proving all other possibilities are wrong. This led us to studying indirect proofs, negations, inverses, and contrapositives. The final thing we learned was triangle comparisons. One can use these to estimate or find the exact length of a side or angle in a triangle with the proper information.