Kites

PROPERTIES OF KITES:
-Diagonals are perpendicular
-When shown as in above diagram:
--The two upper sides are congruent
--The two lower sides are congruent
--The left and right angles are congruent
--When we add the diagonals:
---The horizontal diagonal is bisected by the other diagonal
---The vertical diagonal bisects the two angles it goes through
---Two Isosceles triangles are created
-These properties apply to ALL kites, but sometimes rotated.

Kites are so weird, Khan Academy didn't have a video for them... That was annoying.
So then, I looked at vimeo, because apparently that's the thing that you use at school to get videos because they blocked youtube. I got nothing. Well, I got this video... http://vimeo.com/22253704 but it's not very educational. It's funny, but not educational, unless you're like, six. We're not six. Plus, it's like twenty five minutes... not fun.

Now, apparently I'm not going to post a video, because kites are so bizarre that no one who makes videos cares about them. I have no other ideas, so I'm just gonna write a poem, because things that rhyme tend to be helpful. They just do. Please don't mock my excessively fail poetry.

with perpendicular diagonals
kites can look like pterodactyls. (sort of.)
one diagonal bisects the other
and they form isosceles triangles like brothers.
one diagonal bisects angles
and bisects the diagonal that is the base of the two triangles.
two pairs of sides are congruent
but not opposite sides, 'cause that'd ruin it.
there's a pair of angles that are congruent
they are opposites, but it didn't ruin it.
this poem is really bad, but I don't care
'cause it rhymes, and it sticks in your head, SO THERE.

NEXT SCRIBE hopefully can do better than me... (shouldn't be too hard)
DMITRI! Good luck with that.

Trapezoids!

Today in class, we learned about trapezoids, and how they associate with chapter 5.

All trapezoids have one pair of parallel sides, and they are called the bases. The other two sides are called the legs. The bases are often labeled b1 and b2.

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Isosceles Trapezoid:

They carry many of the characteristics that a regular trapezoid does, but in this kind;

• the legs are congruent
• the base angles are congruent
• the diagonals are congruent
• the angles created by a median (below) are congruent
  

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Median:

• Is a segment that extends from one leg of a trapezoid, to the other.
• A median to a trapezoid divides each leg into congruent segments.
• The formula for finding the median of a trapezoid is [(b1+b2)]÷2
• The median is parallel to b1 and b2.
• If you have an isosceles triangle with a median,than all four segments created are congruent.

And now for an informational video!

http://www.youtube.com/watch?v=d8DAYzbmuBE

And the next student scribe is...................











Hollee! Good luck!

-Love Emma, 11/28/11 (my Birthday!!)

Rectangles, Squares, and Rhombuses

Rectangles, Squares, and Rhombuses (Special Parallelograms)

Prop. of Parallelograms:

• both pairs of opposite sides are parallel
• both pairs of opposite sides are congruent
• the diagonals bisect each other
• both pairs of opposite angles are congruent

Rectangles:

• 4 right angles
• diagonals are congruent
  
• prop. of a parallelogram

Rhombuses:

• all 4 sides are congruent
• the diagonals are perpendicular to each other
• the diagonals bisect opposite angles
• all properties of a parallelogram
  

Squares:

• all properties of a rhombus
• all properties of a rectangle
• all properties of a parallelogram

Always, Sometimes, Or Never

1. If an angle of a parallelogram is a right angle then is it a rectangle?
2. Is a square a rectangle?
3. Is a rectangle a square?
4. If a diagonal bisects 2 angles then is it a square?
5. If the diagonals of a parallelogram are perpendicular to each other then is it a rectangle?

1.always 2.always 3.sometimes 4.sometimes 5.sometimes

HERE ARE SOME HELPFUL VIDEOS

http://vimeo.com/15571270 <- the teacher in that one is a little wacky, but it helps

http://www.5min.com/Video/How-to-Use-the-Properties-of-Special-Parallelograms-516909821

AND THE NEXT SCRIBE ISSSSSSSSS..................

EMMA! (your welcome)

AND THATS IT FOR TONIGHT THANKS FOR READING SPECIAL PARALLELOGRAMS!!!!!

by, Jessica Young

5.2 Proving Quadrilaterals are Parallelograms

Today Ms.Hunt showed us 4 theorems that we can use to prove that quadrilaterals are parallelograms.

Review on Parallelograms: Opposite angles are congruent, opposite sides are congruent, diagonals bisect each other, and both opposite sides are parallel.

Theorem 5.4- If both pairs of opposite sides in a quadrilateral are congruent, then the quadrilateral is a parallelogram. Here is a proof problem that will prove this.


Given: Segment Ts is congruent to segment QR; segment TQ is congruent to segment SR.



Prove: Quadrilateral QRST is a parallelogram.

Statement Reason

1. 1.Given

2. Segment SQ is congruent to segment SQ 2. Reflexive Prop.

3. Triangle QST is congruent to Triangle SQR 3.SSS postulate

4. Angle 1 is congruent to angle 2; Angle 3 is congruent to angle 4 4.CPCTC

5.Angle 1, angle 2, angle 3, and angle 4 are alternate 5. Def. of alt. int. angles

interior angles

6. Segment TS is parallel to QR; Segment TQ is parallel to segment SR

6. If 2 parallel lines are cut by a transversal and alt. int. angles are congruent, the the lines are parallel.

7. QRST is a parallelogram 7. Def. of parallelogram

Here is another theorem

Theorem 5.5- If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

Given: Segment TS is congruent to segment QR; Segment TS is parallel to segment QR.


Prove: Quadrilateral QRST is a parallelogram.

This one was for homework, so I can't write the answer down.

Theorem 5.6- If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.





Given: Angle A is congruent to Angle C: Angle B is congruent to Angle D.


Prove: Quadrilateral ABCD is a parallelogram.


This one was on the homework too, so I'll leave you guys to solve that.


Theorem 5.7- If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.


Given: Segment AM is congruent to segment MC; Segment DM is congruent to segment MB.
Prove: ABCD is a parallelogram.

Another one on the homework! Good luck with this one!

So let's review...
The five ways to prove that a quadrilateral is a parallelogram is to show that...

• Both pairs of opposite sides are parallel.


• Both pairs of opposite sides are congruent.


• One pair of opposite sides are congruent and parallel.


• Both pairs of opposite angles are congruent.


• Diagonals bisect each other.

Our homework for today is Page 174 numbers 1-22, 23, and 24, with 25 being optional for a challenge.

Here is a link for more detailed information, as well as extra practice!

http://www.onlinemathlearning.com/parallelogram.html

http://www.sonoma.edu/users/w/wilsonst/courses/math_150/theorems/Parallelograms/default.html

The next scribe is....

Not Sean, Dmitri, J.D., Zahra, Phil K., Phil J., David, Matt, Katie, Krista, Kerryann, Ms. Hunt, Francis, Emma, myself, Hollee, or Olivia.

It's....

Ashley! Good luck on your next scribing!

Have a nice day!

Review for Chapter 4

Tonight's review was pg. 160 #1-20
Tomorrow we will be reviewing more

Ways to Prove Triangles Congruent

• SSS
• SAS
• ASA
• AAS
• HL (Only use with right triangles)

How to prove parts of two triangles congruent

1. Prove the two triangles are congruent by using one of the theorems/ postulates that proves them congruent
2. Then state that the two parts are congruent by using CPCTC ( Corresponding parts of congruent triangles are congruent)
   

Theorems/ Postulates

• Theorems/ Postulates used to prove triangles congruent (SSS, HL, ASA, etc...)
• Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
• Converse of Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
• If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.
• Converse: If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
• If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.
• Converse: If a point is equidistant from the sides of an angle, then the point lies on the bisector of an angle.

Difference Between Median and Altitude
Median: A segment from the vertex to the midpoint of the opposite side.
Altitude: Perpendicular segment from the vertex to the opposite side.

Reminder
Name triangles so congruent points correspond

Helpful Videos
http://www.khanacademy.org/video/congruent-triangles-and-sss?playlist=Geometry
http://www.khanacademy.org/video/finding-congruent-triangles?playlist=Geometry
http://www.khanacademy.org/video/review-of-triangle-properties?playlist=Geometry

For Chapter Summary pg. 159-160
Test is Wednesday 11/9/11


The next scribe is......... Tim

4.7 Info about segments

4.7 Info about segments

Median: A segment that extends from a vertex to the opposite side

- Segment intersects the side at the midpoint

- 3 per triangle

Altitude: A segment that extends from a vertex to the opposite side

- Creates rt. angles

- 3 per triangle

- Located IN, ON THE SIDE of or OUTSIDE of a triangle.

- If a point lies an a perpendicular bisector of a segment, the point is equidistant to the endpoints of the segment

- Converse is also true

- If an angle bisector contains a point, then the point is equidistant from the sides of the angle (the new segments must be perpendicular to the rays of the angle)

- Converse is also true

VIDEO: http://vimeo.com/16443191

Using More Than One Congruent Triangle In A Proof

Today, we learned about using more than one pair of congruent triangles in a proof. It’s really simple and just added steps to normal proofs. You can use SSS, SAS, ASA, AAS, HL and CPCTC to help through the proof.

Some tips for proofs:

· Remember key steps

· ALWAYS write in 2 column form unless told otherwise

· Make sure your reasons are correct

· Stay neat with proof

· Draw diagrams

· The given is ALWAYS first, the book is wrong, and the point to prove is always lastToday, we learned about using more than one pair of congruent triangles in a proof. It’s really simple and just added steps to normal proofs. You can use SSS, SAS, ASA, AAS, HL and CPCTC to help through the proof.

Some tips for proofs:

· Remember key steps

· ALWAYS write in 2 column form unless told otherwise

· Make sure your reasons are correct

· Stay neat with proof

· Draw diagrams

· The given is ALWAYS first, the book is wrong, and the point to prove is always last

this helps also- http://www.vhstigers.org/ourpages/auto/2006/6/20/1150817470106/Geometry%204-6%20Using%20More%20than%20One%20Pair%20of%20Congruent%20Triangles.pdf