# 2 4 System of Geometry Knowledge

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```					  2.4 – Building a
System of Geometry
Knowledge
Euclid (325 BC – 265 BC)
It’s all Greek to me!
• Greek mathematician
• Lived ≈ 300 BC in Alexandria, Egypt
• Organized existing knowledge of
geometry
• Wrote “The Elements” starting with:
5 basic postulates
• Subtraction
• Division
• Multiplication
• Substitution
Properties
∞You can add the same thing to both
sides
∞ If a = b then a + c = b + c
Properties
• Subtraction Property
∞You can subtract the same thing
from both sides
∞ If a = b then a – c = b – c
Properties
• Multiplication Property
∞You can multiply the same thing to
both sides
∞If a = b then ac = bc
Properties
• Division Property
∞You can divide both sides by the
same thing
∞ If a = b then a / c = b / c
(c cannot = 0 because you cannot
ever divide by 0)
Properties
• Substitution Property
∞If a = b then you can replace a with
b or b with a in any equation
Properties
• Reflexive property (1 thing)
∞ Anything is equal/congruent to itself
∞ A=A
• Symmetric Property (2 things)
∞If A = B, then B = A
• Transitive Property (3 or more things)
∞If A = B and B = C, then A = C
Properties
• Distributive Property
∞ a(b + c) = ab + ac
∞ (b + c)a = ab + ac
(just to see if you remember!)
THEOREM

a statement that has been
proven deductively
Theorems
• Overlapping Segments Theorem
∞Given a segment with points A, B, C
and D arranged consecutively and if
AB = CD then AC = BD and if AC =
BD then AB = CD

A    B        C        D
Theorems
• Overlapping Angles Theorem
∞Given angle AOD with points B and
C in the interior, then if mAOB =
mCOD then mAOC = mBOD
and if mAOC = mBOD then
mAOB = mCOD
B   C
A

D
O

```
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