6 6 Analytic Geometry Coordinate Geometry uses actual

6 -6 Analytic Geometry

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

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

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 using midpoints y y (-b, c) Q P (-a, 0) R (b, c) (2 b, 2 c) S x (2 d, 2 c) (2 a, 0) (0, 0) x

Trapezoid Midsegment Theorem y (1) The midsegment of a trapezoid is parallel to the bases (2) The length of the midsegment of a trapezoid is half the sum of the lengths of the bases. PROVE IT! (2 b, 2 c) (2 d, 2 c) x (0, 0) (2 a, 0)

Analytic Proofs E-Block #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. B 1 #1 Carolyn Gabby #2/3 Christian. P David #4 Jess Kayleigh #5* Alek Nathaniel #5* Josh. S Zoe #6* Tyler John #6* Marissa Hayley #8 Christian. A JB #9 Josh. C Sliker

Analytic Proofs E-Block #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. B 4 #1 Kim Ben T. #2/3 Conner Connor #4 Richard Anna #5* Alan David #5* Rachel Natalie #6* Kevin Jack #6* Nate Mallorie #8 Boo Kasey #9 Ben K Austin