MODULE II VOCABULARYPART I

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!

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!

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.

MODULE II

• Firstly, let’s discuss more about isosceles triangles.

• If we take a look at one of these triangles, what do you notice?

MODULE II

MODULE II

• The angles which touch the base of a triangle are called base angles.

• The base angles of an isosceles triangle are congruent.

MODULE II

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

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.

MODULE II

• What do you notice about this midsegment?

MODULE II

• What about this one?

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.

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.

MODULE II

• These have properties too! Particularly when then intersect!

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.

MODULE II

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