Class of Today

Today we started class by reading theorems 5-9 and 5-10, and going to the computer lab to explore and understand it in GeoGebra.

After that, we came back to class and analyzed the differences between theorems 5-8 and 4-3. While the first states the exterior angle is greater than EACH of the remote interior angles, the other states the exterior angle is equal than the sum (can we call it union?) of BOTH remote interior angles.

Then we made the correction of our howemork (I can't recall the page at the moment, and forgot my notebook at the school).

The major part of the class, though, was about Lesson 5-4 (Inequalities for sides and angles of a triangle), which we came back to discuss afterwards. Theorems 5-8, 5-9, and 5-10 and Corollary 5-1 were what we looked at.

1. With Theorem 5-9, if we have the sides, we are able to compare the angles. It states that if there are two sides, and one longer than the other, the angle opposite the longer side is bigger than the one opposite the shorter side.
2. Theorem 5-10 is the converse of Theorem 5-9. If we have two angles, one bigger than the other, the side opposite the bigger angle is longer than the side opposite the smaller one.
3. Theorem 5-11 states that the shortest possible segment between a line segment and a point not on it is a segment that connects them in 90º - in other words, a perpendicular segment. We learned an extension of it in right triangles, which, unfortunatly, cannot be used in provings (just if you take all steps needed). In those, sides which have the right angles are smaller than the hypothenuse.
4. Corollary 5-1: this is just another kind of extension of Theorem 5-11,which replaces the line segment with a plane. That means, the shortest possible segment between a plane and a point not on the plane is a perpendicular line segment.
   

So, I think that was it.

Just some reminders:
*TOMORROW, we have a QUIZ on lessons 5-1, 5-2 and 5-3
*Also, DON'T forget to start doing the project for thursday ( we are going to have a class on wednesday, in which we can decide to study or develop our projects, but it is nice to start)