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2.3: Proofs
Last Night’s Homework: 2.2 Handout
Tonight’s Homework: 2.3 Handout
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3. Chapter 2 Section 3

10. Multiplication Property Division Property
Addition Property
Subtraction
Property
Multiplication Property
Division Property
If a=b & c≠0,
then a÷c = b÷c
If a=b,
then a+c = b+c
If a=b,
then a-c = b-c
If a=b,
then ac = bc
Reflexive Property
Symmetric
Property
Transitive Property
Substitution Property
If a=b,
then a & b can be switched
For any # a,
a = a
If a=b,
then b=a
If a=b & b=c,
then a = c

11. Two Column Proofs
Allow us to organize arguments using numbering to connect statements with valid reasoning.
Statements
Reasons

12. Two Column Proofs
Statements
Reasons

13. ≅ Complement Theorem:
If two ∠s are complements of the same ∠ or of congruent ∠s, then the ∠ s are ≅.

14. Right Angle ≅ Theorem:
All right angles are ≅
Vertical Angle Theorem:
Vertical angles are ≅.

15. Biconditional Statements
If and Only If Form (iff): A statement using the form “Hypothesis if and only if Conclusion.” (Abrev. iff)
Example:
It’s a right angle iff the angle has a measure of 90°
Essentially a conditional and converse written at same time, must be true “forward” and “backward.”
Conditional:
If it’s a right angle then the angle has a measure of 90°
Converse:
If the angle has a measure of 90° then it’s a right angle.