By Mrs. Lee Huang

A perfect proof must always include the following components (yes, all of them!): 1.A “given” statement – this is your starting point; the fact(s) that you start working with2.A “prove” statement – this is the goal you want to reach/prove3.A picture – a visual that helps you understand the relationship of figures4.A statement & reason, or sTr, chart – the step-by-step logical process that connects the “given” statement to the “prove” statement

Statement

Statements must be numbered. The first statement is usually

the given statement. The statements are written in

“math form” – equations, congruencies, etc.

The statement should match the conclusion of the corresponding reason.

Reason

Reasons must be numbered to match their corresponding statements

The reason for the given statement is always “given.”

All other reasons must be accepted definitions, theorems or postulates written out fully.

The condition/hypothesis, “if” statement, must be met either through previous step(s) or visually in the figure.

1 2 3A●

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● ●

●

O

C

D

B

Show me the logic!

1 2 3A●

●

● ●

●

O

C

D

B

Show me the logic!

1 2 3A●

●

● ●

●

O

C

D

B

Show me the logic!

1 2 3A●

●

● ●

●

O

C

D

B

Show me the logic!

1 2 3A●

●

● ●

●

O

C

D

B

ab

c

a = d

b == c

= d

3. Transitive Property

1 2 3A●

●

● ●

●

O

C

D

B

4. Reflexive Property

a = b

c = d

a – c = b – d 5. Subtraction Property

1 2 3A●

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● ●

●

O

C

D

B

1 2 3A●

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● ●

●

O

C

D

BDraw the “given”

into the figure! It’ll help you visualize the information.

Write the “prove” statement at the

bottom. It can help you to focus on your

next steps.

1 2 3A●

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● ●

●

O

C

D

B

The hypothesis, “if” phrase, of each reason should be met either

through the figure or an earlier statement.

Also, the conclusion, “then” phrase, of each

reason should match the structure of its corres-ponding statement.