If you have been reading my math blog at all, then you know I have been posting my youtube videos here and giving each one a brief description. I am ready to get back in action and prove some angles congruent! One of the easiest ways to prove angles congruent is with knowledge of the Vertical Angles Theorem. The vertical angle theorem states that vertical angles are congruent.
In the proof of the vertical angles theorem, you have to establish a relationship between angles 1 and 3 and angles 2 and 3. Both pairs of angles are are supplementary pairs, thus their sum is 180 degrees, which can be seen in statement 2 of the above proof. Now that statement 2 is established, you can state that the sum of the measures of angles 1 and 3 is equal to the sum of the measures of angles 2 and 3. The previous is shown in statement 3 in the above proof. Now this equation is really cool, because it can be changed into the measure of angle 1 is equal to the measure of angle 2, which is very close to what must be proved. Since the measures are equal, the angles are also congruent. See statements for and 5 in the above prove.
I hope to incorporate this into my class some how. I will get back to you and let you know.