1. Lesson 45 INTRODUCTION TO COORDINATE PROOFS

2. Vocabulary and Some Math Trivia A coordinate proof i s a style of proof that uses coordinate geometry and algebra. Coordinate geometry is also known as analytic geometry w hich is a branch of mathematics that uses algebra to aid the study of geometry. Rene Descartes (1595-1650) is credited for the development of coordinate geometry. The story goes that he was lying in bed observing the movements of flies crawling over tiles on the ceiling. It struck him that he could describe a fly’s position by referring to the intersecting lines of the tiles.

3. Positioning a Figure on the Coordinate Plane Right TriangleIsosceles Triangle

4. Positioning a Figure on the Coordinate Plane Square or RectangleTrapezoid

5. Prove ΔDEF is isosceles

6. Prove KLMN is a Trapezoid

7. Assigning Variables as Coordinates A square has a side length of t. Place the square on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin?

8. A square has a side length of t. Place the square on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis?

9. A square has a side length of t. Place the square on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis? What is the ordered pair on the y-axis?

10. A square has a side length of t. Place the square on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis? What is the ordered pair on the y-axis? What is the last ordered pair?

11. A square has a side length of t. Place the square on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis? What is the ordered pair on the y-axis? What is the last ordered pair?

12. Prove the diagonals are perpendicular

13. Assigning Variables as Coordinates A parallelogram base of m and a height of p. Place the parallelogram on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin?

14. A parallelogram base of m and a height of p. Place the parallelogram on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis?

15. A parallelogram base of m and a height of p. Place the parallelogram on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis? What is the ordered pair of the upper left point ?

16. A parallelogram base of m and a height of p. Place the parallelogram on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis? What is the ordered pair of the upper left point ? What is the last ordered pair?

17. A parallelogram base of m and a height of p. Place the parallelogram on the coordinate plane and label each vertex with an ordered pair. What is the ordered pair at the origin? What is the ordered pair on the x-axis? What is the ordered pair of the upper left point ? What is the last ordered pair?

18. Any Questions?