1. 6-6
Analytic Geometry

2. Coordinate Geometry uses actual points.
Analytic Geometry uses variables; zero is the only acceptable number. You use definitions and formulas (midpoint, distance, and slope).
(0, 0) x y
(a, 0)
(0, b)
Right Triangle
Place a geometric figure in a convenient position on the coordinate plane (usually placing a vertex on the origin).
Scalene Triangle
(0, 0) x y
(b, c)
(a, 0)
(0, 0) x y
(a, b)
(2a, 0)
Isosceles Triangle

3. Analytic Proofs
Place a geometric figure in a convenient position on the coordinate plane (usually placing a vertex on the origin).
(0, 0) x y
(0, 0) x y
Parallelogram
Rectangle using midpoints
(b, c)
(a+b, c)
(0, 2b)
(2a, 2b)
(a, 0)
(2a, 0)
(0, 0) x y
(0, 0) x y
Square
Rectangle w/out midpoints
(0, a)
(0, b)
(a, a)
(a, b)
(a, 0)
(a, 0)

4. Coordinate Proof Example
Given: Trapezoid PQRS Find PQ and SR and verify that PQRS is an isosceles trapezoid Prove that the diagonals are congruent
Isosceles Trapezoid
Trapezoid using midpoints
(0, 0) x y y
(-b, c)
(b, c) Q R
(2b, 2c)
(2d, 2c) P S
(2a, 0)
(-a, 0)
(a, 0) x

5. Trapezoid Midsegment Theoremy
The midsegment of a trapezoid is parallel to the bases
The length of the midsegment of a trapezoid is half the sum of the lengths of the bases.
PROVE IT!
(2b, 2c)
(2d, 2c) x
(0, 0)
(2a, 0)

6. Analytic Proofs
E-Block B1
#6* Marissa Hayley #8
ChristianA JB
#9 JoshC Sliker #1
Sam G
Bobby
#2/3
Kara
Alicia #4
Abby
Aleah
#5*
Deanna
Kasi
*Ask for hint on placement
#6*
Evan
Alex #8
Jess
Floriana #9
Annalee
Sam T. #1
Carolyn Gabby
#2/3
ChristianP David
#4 Jess Kayleigh
#5*
Alek Nathaniel
JoshS Zoe
#6*
Tyler John

7. Analytic Proofs
E-Block B4
#6*
Nate Mallorie #8
Boo Kasey #9
Ben K Austin #1
Sam G
Bobby
#2/3
Kara
Alicia #4
Abby
Aleah
#5*
Deanna
Kasi
*Ask for hint on placement
#6*
Evan
Alex #8
Jess
Floriana #9
Annalee
Sam T. #1
Kim Ben T.
#2/3
Conner Connor #4
Richard Anna
#5*
Alan David #5*
Rachel Natalie
#6*
Kevin Jack