APPLYING POLYGON PROPERTIES TO COORDINATE GEOMETRY 6.7 – 6.8

Our Goals:

 To apply previously learned coordinate geometry formulas

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

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

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

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.

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.

To start

 Let’s talk about the classification of triangles

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

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

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

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

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

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)

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

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

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

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).

Now for quadrilaterals

 Can we do some of them with sides?

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.

Here’s a procedure checklist…

 1) Find the slopes of all 4 sides.

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

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

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

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.

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.

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

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

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

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

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.

Flowchart of the same information.