module ii vocabulary part i. module ii the name of this module is “reasoning and proof”. in this...
TRANSCRIPT
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!
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• 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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• 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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• 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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• 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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• Triangles have all sorts of hidden properties that only someone with a geometry eye can see.
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• 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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• What do you notice about this midsegment?
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• What about this one?
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• 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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• 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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• These have properties too! Particularly when then intersect!
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• 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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• There are many more properties that we will discuss in the coming days. For now, we will focus on these few.