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MODULE II VOCABULARY PART I

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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!

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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!

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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.

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

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MODULE II

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

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

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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.

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MODULE II What do you notice about this midsegment?

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MODULE II What about this one?

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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.

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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.

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

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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.

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

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Chapter 5 Relationships within Triangles In this chapter you will learn how special lines and segments in triangles relate.

Chapter 5 Relationships within Triangles In this chapter you will learn how special lines and segments in triangles relate.

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