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6-6 Analytic Geometry

6-6 Analytic Geometry. y. y. y. Right Triangle. (a, b). (0, b). (0, 0). (0, 0). (0, 0). x. x. x. (b, c). (a, 0). (2a, 0). (a, 0). Coordinate Geometry uses actual points.

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6-6 Analytic Geometry

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  1. 6-6 Analytic Geometry

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

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

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

  5. Trapezoid Midsegment Theorem y • 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*MarissaHayley#8 ChristianAJB #9JoshCSliker #6* Evan Alex #8 Jess Floriana #9 Annalee Sam T. #1 Sam G Bobby #2/3 Kara Alicia #4 Abby Aleah #5* Deanna Kasi *Ask for hint on placement #1 CarolynGabby #2/3 ChristianPDavid #4JessKayleigh #5* AlekNathaniel #5* JoshSZoe #6* TylerJohn

  7. Analytic Proofs E-Block B4 #6* NateMallorie #8 BooKasey #9 Ben KAustin #6* Evan Alex #8 Jess Floriana #9 Annalee Sam T. #1 Sam G Bobby #2/3 Kara Alicia #4 Abby Aleah #5* Deanna Kasi *Ask for hint on placement #1 KimBen T. #2/3 ConnerConnor #4 RichardAnna #5* AlanDavid#5* RachelNatalie #6* KevinJack

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