1. APPLYING POLYGON PROPERTIES TO COORDINATE GEOMETRY 6.7 – 6.8

2. Our Goals:

3.  To apply previously learned coordinate geometry formulas

4. Our Goals:  To apply previously learned coordinate geometry formulas  Coordinate Midpoint Formula

5. Our Goals:  To apply previously learned coordinate geometry formulas  Coordinate Midpoint Formula  Distance Formula

6. Our Goals:  To apply previously learned coordinate geometry formulas  Coordinate Midpoint Formula  Distance Formula  Slope

7. Our Goals:  To apply previously learned coordinate geometry formulas  Coordinate Midpoint Formula  Distance Formula  Slope To the properties of polygons and quadrilaterals discussed in Chapter 6 thus far.

8. If forgotten, these are on page 400 in your book!  To apply previously learned coordinate geometry formulas  Coordinate Midpoint Formula  Distance Formula  Slope To the properties of polygons and quadrilaterals discussed in Chapter 6 thus far.

9. To start

10.  Let’s talk about the classification of triangles

11. To start  Let’s talk about the classification of triangles  If we do so by sides, how can we figure out side lengths?

12. Scalene, Isosceles, Equilateral  Let’s talk about the classification of triangles  If we do so by sides, how can we figure out side lengths?

13. To start  Let’s talk about the classification of triangles  If we do so by sides, how can we figure out side lengths? Distance Formula

14. Page 401  Let’s talk about the classification of triangles  If we do so by sides, how can we figure out side lengths? Distance Formula

15. Page 401  A(0, 1), B(4, 4), and C(7,0) (4, 4) (0, 1) (7, 0)

16. Does it matter which order we do the points?  A(0, 1), B(4, 4), and C(7,0) (4, 4) (0, 1) (7, 0)

17. You try this one  A(0, 1), B(4, 4), and C(7,0) (4, 4) (0, 1) (7, 0)

18. You try this one  Classify  HJK by its sides given the coordinates H(-1,0), J(- 16, -20) and K(-25, 7).

19. You try this one  Classify  HJK by its sides given the coordinates H(-1,0), J(-16, - 20) and K(-25, 7).

20. Can we ever do it without doing all 3 sides?  Classify  HJK by its sides given the coordinates H(-1,0), J(-16, - 20) and K(-25, 7).

21. Now for quadrilaterals

22.  Can we do some of them with sides?

23. Now for quadrilaterals  Can we do some of them with sides?  Sure, but it is going to be a lot easier with slopes, since many of our classifications involve parallel and perpendicular properties.

24. Here’s a procedure checklist…

25.  1) Find the slopes of all 4 sides.

26. Here’s a procedure checklist…  1) Find the slopes of all 4 sides.  No equal slopes  Quadrilateral.

27. Here’s a procedure checklist…  1) Find the slopes of all 4 sides.  No equal slopes  Quadrilateral.  One pair =  Trapezoid

28. Here’s a procedure checklist…  1) Find the slopes of all 4 sides.  No equal slopes  Quadrilateral.  One pair =  Trapezoid  Both pairs =  Parallelogram.

29. Here’s a procedure checklist…  2)If AND only if you have a trapezoid, find the lengths of the 2 non-parallel sides using the distance formula to see if it’s isosceles.

30. Here’s a procedure checklist…  2)If AND only if you have a trapezoid, find the lengths of the 2 non-parallel sides using the distance formula to see if it’s isosceles.  3)If it’s a parallelogram, see if the slopes are negative reciprocals.

31. Here’s a procedure checklist…  2)If AND only if you have a trapezoid, find the lengths of the 2 non-parallel sides using the distance formula to see if it’s isosceles.  3)If it’s a parallelogram, see if the slopes are negative reciprocals. Rectangle

32. Here’s a procedure checklist…  3)If they’re not negative reciprocals, check the slopes of the diagonals.

33. Here’s a procedure checklist…  3)If they’re not negative reciprocals, check the slopes of the diagonals.  If the slopes of the diagonals are negative reciprocals  Rhombus

34. Here’s a procedure checklist…  4)Even if the slopes are negative reciprocals, you are checking the slopes of the diagonals.

35. Here’s a procedure checklist…  4)Even if the slopes are negative reciprocals, you are checking the slopes of the diagonals.  Rectangle with perpendicular diagonals is a square.

36. Flowchart of the same information.