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.

11) 7X=49

12) 3X-8=19

13) X/6 = 3

14) X(7+3)=100

15) X+3=10

16) X-5=30

17) (X/8)+6=4

18) X*(A+B)=C

19) 2X=2X