Writing a Proof

1
Writing a Proof

• A proof a convincing argument that shows why a
  statement is true.
• A two-column proof has numbered statements and
  reasons that show the logical order of the
  argument.
• Each statement has a reason listed to its right.

2
How to Write a Proof

• List the given information first.
• Use information from the diagram.
• Give a reason for every statement.
• Use given information, definitions, postulates,
  and theorems as reasons.
• List statements in order. If a statement relies
  on another statement, list it later than the
  statement it relies on.
• End the proof with the statement you are trying
  to prove.

3
Write a Proof

• Write a two-column proof that shows JKL
  NML.
• Given JL NL
• L is the midpoint of KM.
• Prove JKL NML
• Solution The proof can be set up in two
  columns. The proof begins with the given
  information and ends with the statement you are
  trying to prove.

J

K
M
L

N
4

• Statements Reasons
• S 1. JL NL 1. Given
• 2. L is the midpoint 2. Given
• of KM.
• A 3. JLK NLM 3. Vertical Angles
• Theorem
• S 4. KL ML 4. Definition of
  midpoint
• 5. JKL NML 5. SAS
  Congruence Postulate

5
More Practice!!!

• Textbook p. 244 1, p. 247 248 34, 35, 36.