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Overlapping Triangles - Lesson 3-5

We didn't really learn much new today...rather, we just applied what we've already learned to triangles that are overlapping and therefore sharing some part(s).  An example is below:

We also went over the following example...can it be proved?

As we saw, we only have SSA here, which we know doesn't work (unless the triangle is a right triangle!).  Clearly, in the diagram below, the triangles aren't congruent, even though the same parts are congruent!.  Wouldn't it be nice if you had Sketchpad and a SmartBoard on your tests so that you could play with the figures like we can in class?!?

Before going over homework, we also went through the following example...does it work?

As we saw, it does...I've pulled out the two triangles (in red and green below) because it sometimes helps to look at them in this way...

Make sure to do all your homework as these things really take a lot of practice to get used to "seeing" the correct triangles...