Chapter six Marina R

Marina Richardson, Oct 13, 2017

Table of Contents

  1. 6-1
    1. Regular Polygon Action!
    2. sum of interior angles
    3. Exterior angles 360
  2. 6-2
    1. Parallelogram Diagonals
    2. Playing with Parallelograms!
    3. Bisecting diagonals
  3. 6-3
    1. Parallelogram: Theorem 2
    2. Parallelogram: Theorem 1
  4. 6-4
    1. properties of a rectangle
    2. properties of a square
  5. 6-5
    1. Rhombus Template with Investigation Questions
    2. 5.6 Investigation 2
  6. 6-6
    1. Isosceles Trapezoid Template
    2. Kite Template: Scaffolded Investigation
  7. 6-7
    1. Perpendicular Lines Investigation (VB)
    2. Distance in the Coordinate Plane
  8. 6-8
    1. Co-ordinates of Points
    2. 5 coor.
  9. 6-9
    1. coordinate proofs #2
    2. Triangles Coordinate Proofs Example

1.

6-1

  • 1. Regular Polygon Action!
  • 2. sum of interior angles
  • 3. Exterior angles 360

1.1.

Regular Polygon Action!

The applets below illustrate what it means for any polygon to be classified as a [b]regular polygon.[br][/b][br]In these applets, a pentagon and a triangle will be used to illustrate this definition.[br][br]Interact with these applets for a minute or two, then answer the questions that follow.
REGULAR PENTAGON
REGULAR TRIANGLE
1.
What does it mean for a polygon to be classified as a [b]REGULAR POLYGON? [/b] [br][color=#0000ff](Feel free to click [b][url=https://www.geogebra.org/m/dSyyZeSS]here[/url][/b] and/or [b][url=https://www.geogebra.org/m/J49qEHYn]here[/url] [/b]for a hint.)[/color]
2.
What is the common name (or most specific name) people give to describe a [b]regular quadrilateral? [br][/b]Why is this?
– Tim Brzezinski

1.2.

–

1.3.

–

2.

6-2

  • 1. Parallelogram Diagonals
  • 2. Playing with Parallelograms!
  • 3. Bisecting diagonals

2.1.

Parallelogram Diagonals

[color=#000000]Use coordinate geometry to prove that the [b]diagonals of a parallelogram bisect each other. [/b] [br][/color][color=#000000]That is, write a coordinate geometry proof that formally proves what this applet informally illustrates. [br][br]Be sure to assign appropriate variable coordinates to your parallelogram's vertices! [br](The maximum number of variable coordinates your coordinate setup should have is 3.)[/color]
[color=#000000]Now prove this same theorem true using the format of a 2-column proof or a paragraph proof.[br][/color][i][color=#000000]Hint: This proof may contain multiple pairs of congruent triangles. [/color][br][br][/i][color=#1e84cc]In your opinion, was this theorem easier to prove using a coordinate geometry setup OR a paragraph (or 2-column) proof setup? What do you think? [/color]
– Tim Brzezinski

2.2.

–

2.3.

–

3.

6-3

  • 1. Parallelogram: Theorem 2
  • 2. Parallelogram: Theorem 1

3.1.

Parallelogram: Theorem 2

Interact with the applet below for a few minutes. [br]Then, answer the questions that follow. [br][br]Feel free to move the BIG WHITE POINTS anywhere you'd like! [br][color=#ff00ff]You can also adjust the size of the pink angle by using the slider. [/color]
1.
What special type of quadrilateral was formed in the first half of your sliding-the-slider? How do you know this?
2.
What else can you conclude about this special type of parallelogram? Be specific!
3.
In the special quadrilateral above, [color=#ff00ff]suppose the pink angle measures 110 degrees[/color]. [color=#0000ff]What would the measure of the blue angle be?[/color] What would the measure of each interior angle of this special quadrilateral be?
4.
Write a 2-column or paragraph proof of what you've informally observed here. (Hint: This proof will involve a pair of congruent triangles!)
Quick Demo: 0:33 sec to 1:16 sec (BGM: Andy Hunter)
– Tim Brzezinski

3.2.

–

4.

6-4

  • 1. properties of a rectangle
  • 2. properties of a square

4.1.

properties of a rectangle

properties of a rectangle
– sonom

4.2.

–

5.

6-5

  • 1. Rhombus Template with Investigation Questions
  • 2. 5.6 Investigation 2

5.1.

Rhombus Template with Investigation Questions

[color=#cc0000][b]Students: [/b][/color][br][br]The applet below contains a quadrilateral that [color=#1e84cc][b]ALWAYS remains a rhombus.[/b][/color] [br]Be sure to move the BIG WHITE VERTICES of this rhombus around as you answer each investigation question! [br][br][color=#cc0000][b]Teachers: [/b][/color][br][br]A PDF copy of this investigation & its questions can be found below the applet.
Rhombus Scaffolded Investigation
– Tim Brzezinski

5.2.

–

6.

6-6

  • 1. Isosceles Trapezoid Template
  • 2. Kite Template: Scaffolded Investigation

6.1.

Isosceles Trapezoid Template

[color=#cc0000][b]Students: [/b][/color][br][br]The applet below contains a quadrilateral that [color=#1e84cc][b]ALWAYS remains an ISOSCELES TRAPEZOID.[/b][/color][br][br]Be sure to move the [color=#1e84cc][b]BIG BLUE VERTICES[/b][/color] of this [color=#1e84cc][b]ISOSCELES TRAPEZOID[/b][/color] around as you answer each investigation question!
– Tim Brzezinski

6.2.

–

7.

6-7

  • 1. Perpendicular Lines Investigation (VB)
  • 2. Distance in the Coordinate Plane

7.1.

Perpendicular Lines Investigation (VB)

[color=#cc0000][b]Students:[/b][/color][br][br]Please use this applet to complete the [b]Perpendicular Lines Investigation[/b] you received at the beginning of class. Note that line f and line g are always perpendicular (intersect to form a right angle)! [br][br]Note: The [color=#1e84cc][b]BIG BLUE POINTS[/b][/color] can be dragged anywhere you like.
– Tim Brzezinski

7.2.

–

8.

6-8

  • 1. Co-ordinates of Points
  • 2. 5 coor.

8.1.

Co-ordinates of Points

Move each point to the correct co-ordinates
Co-ordinates of Points
Click the refresh button to try again with different points
– GreenMaths

8.2.

–

9.

6-9

  • 1. coordinate proofs #2
  • 2. Triangles Coordinate Proofs Example

9.1.

coordinate proofs #2

– Leslie Le

9.2.

–

Information