STYLES OF PROOFS

1
STYLES OF PROOFS

• 3 STYLES OF PROOFS
• PARAGRAPH
• FLOW
• TWO - COLUMN

2
3 THEOREMS

• T 3.3 IF 2 LINES ARE , THEN THEY INTERSECT TO
  FORM 4 RIGHT ANGLES.
• T 3.4 ALL RT ltS ARE .
• T 3.5 IF 2 LINES INTERSECT TO FORM A PAIR OF
  ADJACENT ltS THEN THE LINES ARE PERPENDICULAR.

3
PARAGRAPH PROOF

• WRITTEN AS A NARATIVE
• EXPLAINS THE REASONS IN SENTENCES.

4
PARAGRAPH PROOF THEOR. 3.3

• GIVEN l1 l2
• PROVEmlt1mlt2mlt3mlt4900
• ANGLE 1BY DEFN OF LINES, YOU KNOW THAT THE
  LINES INTERSECT TO FORM RTltS. BY DEF OF RTlt YOU
  KNOW THAT THE lt1 900

1
1
1
1
2
3
4
5
PROOF CONTINUED

• lt4 BY THE VERTICAL ANGLES THEOREM, YOU KNOW THAT
  lt1 lt4. THERFORE, mlt4 mlt1 900.
• lt2 lt1lt2 FORM A LINEAR PAIR AND ARE THEREFORE
  SUPPLEMENTARY. THUS mlt1mlt2 180, SO mlt2 900.

6
PARAGRAPH PROOF CONTINUE

• lt3 lt1 lt3 ALSO FORM A LINEAR PAIR. USING A
  SIMULAR ARGUMENT AS lt2, YOU CAN CONCLUDE THAT mlt3
  900.

7
FLOW PROOF THEOREM 3.4

• SEE PAGE 127

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2 COLUMN PROOF

• GIVEN lt1 lt2, lt1 AND lt2 ARE LINEAR PAIRS.
• PROVE l1 l2

l
1
1
2
l
2
9

• lt1 lt2
• mlt1 mlt2
• lt1lt2 ARE A LINEAR PAIR
• mlt1mlt2180
• mlt1mlt11800
• 2(mlt1)1800

• GIVEN
• DEF. ltS
• GIVEN
• LINEAR PAIR POSTULATE
• SUBSTUTUION
• DISTRIBUTIVE PROPERTY

10

• 7. mlt1 900
• 8. lt1 IS A RIGHT lt
• 9. l1 l2

• 7. DIVISION PROPERTY
• 8. DEF. RIGHT ANGLES
• 9. DEF. PERPENDICULAR LINES