Thursday, April 16: Exterior Angle Theorem

Today we learned the Exterior Angle Theorem.  In crazy confusing "mathy" terms,

The measure of the exterior angle of a triangle is equal to the sum of the measures of the non-adjacent interior angles.

The notes we took in class were very helpful on this one!  We took some triangles and started by tracing them our notebooks.  Then we tore 2 of the vertices off and moved them down to the third vertex and noticed something interesting...

THE 3 VERTICES OF A TRIANGLE ARE SUPPLEMENTARY!

We discussed this and realized we kind of already knew this, since we know the interior angles of any triangle always add up to 180^o (Triangle Sum Theorem). Like I said, we kind of knew this, but we never really connected this to the angles being supplementary.

We took another triangle and did the same thing, but this time we put both of the non-adjacent angles (angle A and angle B below) and laid them next to each other.  From here we determined what that crazy math theorem was actually saying made sense!

The measure of the exterior angle of a triangle is equal to the sum of the measures of the non-adjacent interior angles.

So, in other words, the measure of the angle that supplementary to Angle C (the Exterior Angle to Angle C) is equal to the measures of Angle A plus Angle B!  So the sum of Angle A and Angle B is equal to the Exterior Angle to Angle C.  

There was no new homework tonight- we had a lot of students gone for ISAT testing, so we focused mainly on making sense of this new theorem and then we spent the rest of class working on the maps that are due tomorrow.

We will also have a short quiz on Angle Relationships tomorrow, so if you have ANY questions, please be sure to ask!

 

Wednesday, April 15

No new notes today!  We're gong to take what we've learned this week and apply it in different activities.

The first one is an in-class activity.  If you were not in class today, don't worry about completing this one!  :-)

Tonight assignment is a project you will be working on today and tomorrow.  You will create a map of Parallel City using the angles relationships we've recently learned.

This assignment is a project, so it's worth more than a typical homework.  It is due Friday, and it will be graded on accuracy and creativity.

Click here for the map activity.  Use a piece of construction paper or plain printer paper to complete this project.  Remember, it will be graded like a quiz, so do your best!

Monday, April 13: Angle Relationships

Today we learned about Supplementary Angles, Complementary Angles, Vertical Angles, and Adjacent Angles.

We started by defining each on a piece of paper we folded into fourths.  Then we created an example for each and discussed each relationship.

Supplementary Angles: the sum of their measures is 180^o.

Complementary Angles: the sum of their measures is 90^o.

Vertical Angles:  Angles that are across from each other than share a vertex are congruent.

Adjacent Angles: Angles that share a common side and a vertex.  Adjacent angles are not necessarily congruent.

Examples of each are shown below in the notes we took in class.

Click here for today's homework.