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!

Tuesday, April 14: Transversals

Today we learned about Transversals, and more specifically, the angles that are created when a transversal cuts through 2 or more parallel lines.

There are 3 new angle relationships we learned today:

• Corresponding Angles

• Alternate Interior Angles

• Alternate Exterior Angles

We created a flip book for each of the new relationships (see below).  We found that Corresponding Angles, AIA, and AEA are all congruent.

Front of Flip Book Notes

Inside of Flip Book Notes

Tonight's homework was to finish the Angles Packet that was passed out yesterday.

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. 

Friday, April 10: Quiz, and Introduction to Angles

Today we took a short quiz on Rational Numbers.  If you were not here today, make sure you take this quiz on Monday!

We started our unit on angles, and today we used protractors and practiced measuring angles.  See notes below:

We started by drawing the given angles using a protractor.

Then we measured angles and defined angle terms.

We had a quick homework assignment that most students finished in class.  This is due MONDAY for those students that did not complete it before we left for the weekend.

Click here for today's homework. 

March 10: Converse of Pythagorean Theorem

Today we looked at the Converse of the Pythagorean Theorem.

Before we do that, let's consider what the Pythagorean Theorem is, because it's not JUST a² + b² = c²

The Pythagorean Theorem can be written as follows:

If a triangle IS a right triangle, then a² + b² = c².

The Converse states:

If a² +b² = c², then the triangle IS a right triangle.

Wait... isn't that the same thing?

Nope!  Think about it this way:

If it's the weekend, then we don't have school.  

What is the converse of that statement?

If we don't have school, then it's the weekend.

Is that true?  Not necessarily!  So the converse of the Pythagorean Theorem may at first seem like the exact same thing, but it really isn't!

We can use the converse to determine if a triangle is a right triangle.  If we know the side lengths, we put them into the formula and determine if the sides do in fact create a right triangle!

Click here for tonight's homework.  

March 9: Triangle Investigation

I was gone today, so our guest teacher had an investigation for Pre-Algebra today.  Students were to cut out squares of varying sizes, and use the sides of the squares to create triangles and record the data on the sheets given.

There are many relationships with triangle side lengths and the types of triangles that are created- specifically acute, obtuse, and right triangles.

Click HERE to manipulate a triangle and change it from acute to obtuse to right!

Tomorrow we will look at the relationships we noticed and see what conjectures we can make!

See you tomorrow!