Geometric Proofs

Geometric Proofs

Two Column Proofs

What is a Proof?

A Proof is a convincing mathematical argument.

......(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.

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 )

Other terms...

Space- the set of all points

Geometric Figure- Any collection of points

Multiple Select

Check all that are intangible concepts

• 3 D Box

• Plane

• Line

• sphere

• point

CONPONENTS OF A PROOF

Geometric Proof premises

• Definitions

• Postulates

• Properties

• previous proven theorems

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.

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.

Multiple Choice

A convincing mathematical argument.

• Postulate

• Proof

• Geometric Figure

• Definitions

Writing a Proof

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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.

Follow these steps....

• 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

LET'S DO SOME EXAMPLES!