Beginning Proofs - Lesson 1-4
Today, we began started by defining what a theorem was:
We then talked about our first theorem and proved it using a two-column proof. Note that the theorem is straight forward, as should be the proof. Remember that we can only use previously proved theorems and definitions...that's why all the steps here. However, now that we've proved this theorem, we can use it to prove other theorems! Also - start to get comfortable with this style of proof - we'll be using it extensively throughout the year!! Woohoo!!
One item of note: See how the hypothesis of our last reason below is drawn from previously justified statements and how the conclusion is the same as the statement it is justifying. This is a very common pattern you'll see all year...get used to it and learn to use it!!
At this point, we stated Theorem 2 and proved it as well...it should look very similar to the previous one!
We then used the first of these theorems in another proof. Note that things like addition are "all good" to use as the reason in a proof.
We concluded by going
over the assignment for the line design project...good luck!!