In the seventeenth century, the French mathematician
Rene Descartes applied algebraic principles to geometric situations.
This blending of algebra and geometry is referred to as
analytic geometry. Because this process
often involves placing geometric
figures in a coordinate plane, it is also more commonly known as
coordinate geometry.
Coordinate geometry proofs employ the
use of formulas such as the Distance Formula, the Slope Formula and/or the Midpoint Formula
as well as postulates, theorems and definitions.
When developing a coordinate
geometry proof:

1. draw and label the graph 
2. state the formulas you
will be using 
3. show ALL work (if
you are using your graphing
calculator, be sure to show your screen displays
as
part of your work.) 
4. have a concluding
sentence stating
what you have proven and why it is true. 

Example 1:
Given:
Prove:
is isosceles 
Read the question carefully. The word
isosceles, by definition, tells you that you are looking for
two congruent sides. Since congruent implies "of equal
length" and the word length implies
"distance", you will use the Distance Formula. 

Draw a neat, labeled graph for the problem.


State the formula that you will be using. 

Show ALL work!! Since we are looking for two
sides of equal length, you can STOP when you find the two sides.
Look at the figure before you begin and choose the two sides that
you "think" are of equal length. 
The triangle is isosceles because it has two
congruent sides. 
End with a concluding sentence stating WHY you
know the triangle is isosceles. 
Example 2:

Read the question
carefully. The word trapezoid, by definition,
tells you that you are looking for a figure with ONLY ONE set of
parallel sides. Lines are parallel when they have
the same slope. You will use the Slope Formula. 

Draw a neat, labeled graph for the problem.


State the formula that you will be
using. 

Show ALL work!! We are
looking for ONE set of parallel sides AND one set on nonparallel
sides. Be sure to state the connection between the slopes and the
sides being parallel or nonparallel. 

End with a concluding sentence stating WHY you
know the figure is a trapezoid. 
