generic square

crook problem

coordinate proof

 

 

Point A= -12,6

Point B= 12,3

Point C=-12, 0

Point D= 12, -3

 

Coordinate Proof

Slope of sides AB: slope=6-3-12-12  = ⅛

Slope of side CD: slope = (0+3)/(-12-12)=⅛

CD is parallel to AB

ABCD is a parallelogram

If a quadrilateral has two pairs of parallel sides then it is a parallelogram

Midpoint of Diagonals

CA=-12+12/2, 0+3/2 = (0, 3/2)

BD= -12+12/2, 6-3/2 = (0, 3/2)

Same midpoint of diagonals

If diagonals have the same midpoint then they bisect each other

If a quad has diagonals which bisect each other, then it is a parallelogram

Slope of sides

AB = ⅛

Side AC = undefined

Sides are not opposite reciprocals of each other, therefore not right angles

If a parallelogram has no right angles, then it can’t be a rectangle

Therefore: The quad is a parallelogram

parallelogram

Parallelogrom This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com yours truly, 17 December 2013, Created with GeoGebra

rhombus

I created this rhombus by making congruent segments and constructing lines parallel to them.

Rhombus This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com yours truly, 16 December 2013, Created with GeoGebra

Geogebra Loves the Eagles

The Dude hates Geogebra because Geogebra
loves the Eagles

Although, a Geogebra parallelogram could really
tie the room together.

What are we talking about?

You're out of your element Donny. 

 

Geogebra didn't work so...

Geogebra is being difficult for you, isn't it Mr. Torrance.

Yes it is, what do you suggest I do Delbert.

I feel you will have to deal with this matter in the harshest possible way.
When Geogebra didn't work for me I corrected it.

There's nothing I look forward to with
more pleasure, Mr. Grady

Little Geogebra, Little Geogebra, let me create a simple parallelogram without deleting it before I can upload it.









HERE'S JOHNNY!

   GEOGEBRA! Get back HERE! I need to make        a Parallelogram

 WAIT! GEOGEBRA WAIT!
I NEED YOU TO WORK!

 All Work and No Play make Nate a dull boy.

HW 12/9/13

#math #tbt #blogpost5 #geometry #mrsgalvansclass #hashtag

Lab

Conjecture 1: All pairs of segments on the perpendicular bisector are congruent
Conjecture 2:If a seg forms right and angles and bisects, it is a perpendicular bisector.

Jing

It's a right angle!!!!!!!!!

Reflection Activity

I reflected the triangle over the line which starts in the bottom left of the image. The reflection overlaps the original image, but is pointing the opposite way. All the points are on opposite points on the same Y coordinate. The shift is a 180 degree flip. 

A: (6,0) B: (-2,3) C: (-1,-3)

A': (-6,0) B': (2,3) C: (1,-3)

X=0

I reflected this shape over the center line. The shapes overlap to except for at the ends. They both have the same Y coordinates. The shift is a 180 degree flip.
A,B,C,D
A'B'C'D'
X=0

I reflected the rectangle over the top line. This reflection barely overlaps and is congruent with the other shape. The shift is an upward turn forming an acute angle between the two shapes.

A,B,C,D

A'B'C'D

Y=4

Chain of Reasoning

Chain of Reasoning

If chocolate is good, then people fight over it.
If people fight over chocolate, someone will get hurt.
If someone gets hurt, they will have to wear a bandage.
If someone wears a bandage, they will get sympathy.
If someone gets sympathy for wearing a bandage, they will fake an injury.
If you fake an injury, then someone will find out.
If someone finds out, then they will be mad.
If someone is mad at you, you will be sad.

Therefore: If chocolate is good, then you will be sad.