1. MODULE II VOCABULARY PART I

2. MODULE II The name of this module is “Reasoning and Proof”. In this module, we will begin a deeper understanding of proofs. I WANT THE PROOF!

3. MODULE II A proof is a mathematically sound method for showing something is true. So far, you’ve done informal proofs. HE’S PROOFING INFORMALLY LIKE US!

4. MODULE II You were all able to tell me that a certain figure was a square because of the length of its sides and the measure of its angles. Now, we can prove more about triangles and discover more about quadrilaterals.

5. MODULE II Firstly, let’s discuss more about isosceles triangles. If we take a look at one of these triangles, what do you notice?

6. MODULE II

7. The angles which touch the base of a triangle are called base angles. The base angles of an isosceles triangle are congruent.

8. MODULE II Triangles have all sorts of hidden properties that only someone with a geometry eye can see.

9. MODULE II For instance, let’s take a look at midsegments. A midsegment is a line that connects two of the midpoints of two sides.

10. MODULE II What do you notice about this midsegment?

11. MODULE II What about this one?

12. MODULE II The truth of the matter is that all midsegments are parallel to the third side of the triangle. It will also be half the length of that side.

13. MODULE II Finally, we’ll discuss a median of triangles. A median is a line that connects a midpoint of the sides and the opposite vertex.

14. MODULE II These have properties too! Particularly when then intersect!

15. MODULE II The point at which call these lines meet is called the centroid and it is the center of gravity of a triangle. That just means I could balance that triangle on the tip of my finger.

16. MODULE II There are many more properties that we will discuss in the coming days. For now, we will focus on these few.