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Geometric Proofs
42 minutes ago by
Harvey Williams
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• Slide 1
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Geometric Proofs

Two Column Proofs

• Slide 2
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What is a Proof?

A Proof is a convincing mathematical argument.

• Slide 3
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......(YES WRITE THIS DOWN)

This means that any person, who understands the terminology, accepts the definition and premises of the mathematics involved and thinks in a logical correct fashion could not deny the validity of the conclusions drawn.

• Slide 4
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Undefined Terms-

Can be described but not given precise definitions using simple known terms .

Point

Line

Plane

These are intangible concepts that serve as a foundation. (Used for visualization )

• Slide 5
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Other terms...

Space- the set of all points

Geometric Figure- Any collection of points

• Question 6
45 seconds
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Q.

Check all that are intangible concepts

3 D Box

Plane

Line

sphere

point

• Slide 7
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CONPONENTS OF A PROOF

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• Slide 8
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Geometric Proof premises

• Definitions

• Postulates

• Properties

• previous proven theorems

• Slide 9
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Theorems

Results that we declare from the undefined terms, definitions, postulates , or results that follow from them are call a Theorem

Theorem- is a mathematical Statement that can be proven.

• Slide 10
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Postulate

Postulates are statements that we assume to be true.

An postulate states relationships among defined and undefined terms. The purpose stating postulates is to establish some first principles upon which the subject of geometry is based.

• Question 11
30 seconds
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Q.

A convincing mathematical argument.

Postulate

Proof

Geometric Figure

Definitions

• Slide 12
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Writing a Proof

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• Slide 13
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Writing a Proof

• Justify each logical step with reason.

• You can use symbols and abbrev, but they must be clear and able to understand.

• Slide 14
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• Slide 15
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• Slide 16
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• Step 1 - Write the conjecture (an opinion or conclusion formed on the basis of incomplete information.)

• Step 2 - Draw the diagram

• Step 3 - State the Given information and mark it on the diagram

• Step 4 - State the conclusion of the conjecture in terms of Diagram

• Slide 17
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LET'S DO SOME EXAMPLES!

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