Thinking Geometrically:

1
Thinking Geometrically

• Using Proofs

2
Lesson 4 Axioms or Common Notions

• Axiom 1 Things that are equal to the same thing
  are equal to each other.
• (Think of this as substitution.)
• Example
• 1 yard 3 feet
• 1 foot 12 inches
• 1 yard 3 (12 inches) 36 inches

3
Lesson 4 Axioms or Common Notions

• Axiom 2 If equals are added to equals, the sums
  are equal
• Example
• x - 3 10
• 3 3
• x 13

4
Lesson 4 Axioms or Common Notions

• Axiom 3 If equals are subtracted from equals,
  the differences are equal.
• Example
• x 3 10
• -3 -3
• x 7

5
Lesson 4 Axioms or Common Notions

• Axiom 4 Things that are alike or coincide with
  each other are equal to one another.
• Example

upper
lower
6
Lesson 4 Axioms or Common Notions

• Axiom 5 The whole, or sum, is greater than the
  parts.
• Example