Section 2 - Reasoning
Geometric reasoning consists of 5 basic forms of reasoning. They can be written as theorems using algebraic equation. These are the most often used theorems in geometry.
IDENTITY - If you have A, then A = A. Everything is equal to itself.
SYMMETRY - If A = B, then B=A. Equal quantities are equal even when reversed.
DISTRIBUTIVE - If A*(B+D)=C, then AB + AD=C. Same as distributive property from Algebra.
SUBSTITUTION - If A = C and A = B and C = D, then B = D. If two quantities are equal, they can be substituted for each other.
TRANSITIVE - If A=B and B=C, then A=C. Shortened form of substitution.
There are also four algebraic forms of reasoning used in geometry.
ADDITION - If A-B=C, then A = C+B
SUBTRACTION - If A+B=C, then A=C-B
MULTIPLICATION - A/B=C, then A=CB
DIVISION - If AB=C, then A=C/B
All of these ideas will be used in the future to prove ideas.
Time to practice.
Identify the reasoning used to prove each theorem:
1) If 7=A and 7=B, then A=B
2) If 3X=9, then X=3.
3) If X/4=12, then X=48
4) If you have 10, then 10=10.
5) If X-8=10, then X=18
6) If A=2, then 2=A
7) If A=5 and B=C and A=B, then 5=C.
8) If X+3=10, then X=7.
9) If X*(8-3)=4, then 8X-3X=4.
10) If 7X=AB, then AB=7X.
Solve each equation for X, identifying the form of reasoning used for each step.
13) X/6 = 3
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