1. Proofs Using Coordinate Geometry

2. How Does a Coordinate Proof Work?
Proofs using coordinate geometry use the slope, midpoint, and distance formulas to proof rules and theorems.

3. Ex: Prove a Rectangle Has Congruent Diagonals
Step 1: Place the figure on the xy-axis Step 2: Correctly label the points Step 3: Write a Given and Prove statement Step 4: Use slope, mp, or distance formulas Step 5: Write a concluding statement
( 0 , b )
( a , b ) B C D A
( 0 , 0 )
( a , 0 )
Given: ABCD is a rectangle
Prove: Diagonals are =
(AC=BD)
AC and BD have the same length. Therefore the diagonals of rectangles are congruent.

4. What types of proofs can be done with C.G.?
The slope formula can show:
Segments are parallel.
Segments are perpendicular.
A figure has right angles.
The distance formula can show:
Segments have the same length
Two segments bisect each other
The midpoint formula can show:
The location of a midpoint
Two segments bisect each other.

5. Deciding whether C.G. will work on a Proof.
State whether each of the following can be determined with coordinate geometry.
EF=GH
Yes, with the distance formula
BD ll AC
Yes, with the slope formula
<A=<B
No, unless both are right angles
FG bisects JG
Yes, with the distance or midpoint formulas

6. Deciding whether C.G. will work on a Proof.
State whether each of the following can be determined with coordinate geometry.
Triangle LMN is isosceles
Yes, with the distance formula
The diagonals of Kite QRST are perpendicular
Yes, with the slope formula
<C and <D are supplementary
No.

7. Homework
P 335 (12-24)
Worksheet - Proofs Using the Coordinate Plane