APPLYING POLYGON PROPERTIES TO COORDINATE GEOMETRY 6.7 – 6.8.

APPLYING POLYGON PROPERTIES TO COORDINATE GEOMETRY

6.7 – 6.8

Our Goals:

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

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).

25

20

15

10

5

-5

-10

-15

-20

-25

-50 -40 -30 -20 -10 10 20 30 40 50

J

K

H

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).

25

20

15

10

5

-5

-10

-15

-20

-25

-50 -40 -30 -20 -10 10 20 30 40 50

J

K

H

Now for quadrilaterals

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…

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.