Triangle Sum

# 5.1

• (1-8) all
• we didn't go over this in class today, but I am assigning it anyway because most, if not all, of you guys know that the sum of all 3 angles of a triangle is 180 degrees. That's it. Nothing to it. I won't actually assign the SSS and SAS homework until tomorrow night. I hope that this is ok with all of you, but if it isn't, oh well. You'll get over it. I already have. :o)

The Ch. 4 Practice Test is below!!!!!

Ch. 4 Practice Test

Download the Ch. 4 Practice Test and Solutions. Then do the practice test over and over and over again until you know it like the backs of your hands. THE actual Ch. 4 Test will be given on Monday, March 5, 2006.

Answers for triangle SAD

Congratulations to the Asian Duo (Chen and Jihye), Sabrina B., and Mario B for all coming up with the correct answers to tonight's homework. You guys ROCK!! For the rest of you who are not sure, here they are:


circumcenter:

• (73/38, 132/19)

orthocenter:

• (3/19, 2/19)

centroid:

• (4/3, 14/3)

Euler Line:

• y = 260/67 x - 34/67

Finding Intersections of Lines Part 3

Locate the centroid, circumcenter, and orthocenter of triangle SAD if:

1. S (6, 4)
2. A (1, 2)
3. D (-3, 8)

Then write the equation of the Euler Line. There will be a quiz just like this tomorrow! Use the solutions I gave you today as a model of how to do tonight's homework. If you don't know what you're doing, then post a question here.

Triangle Center Answers

Circumcenter: ( -35/22, -25/66)

• the perpendicular bisector of :
• EO: y = -7/3 x + 10/3
• GO: y = 4/3 x - 5/2
• GE: y = -10/9 x + 65/18

Orthocenter: ( 31/11, 322/33)

• altitude from:
• G to EO: y = -7/3 x + 49/3
• E to GO: y = 4/3 x + 6
• O to GE: y = -10/9 x + 116/9

Centroid: (2, 3)

Euler Line: y = 223/237 x + 265/237

Finding Intersections of Lines Part 2

Locate the centroid, circumcenter, and orthocenter of triangle GEO if G(4, 7) E(-6, -2), O(8, 4).

Then write the equation of the Euler Line using those 3 points. Have fun!

Have a PG - 13 weekend!

Finding Intersection of Lines

# 4.6

• Complete Investigation 4.6
• You MUST find the centroid for triangles ABC, DEF, and GHI.
• Only then will you be allowed to use the shortcut for triangle JKL
• (1-14) all omit #12
  
  
  Don't forget that your Construction Books are due tomorrow!

Construction Book

I thought I posted the homework before I left school, but apparently it didn't go through or something. Hmmmmmm..... don't know what happened. At any rate, because of the late posting, the only fair thing to say is that you should be thankful that you have an extra night to catch up on either last night's homework or the Construction Book Project. Enjoy the semi-night off!

Study Group

I LOVE the fact that Kristina (and a few others) are trying to get this study group idea off the ground so I am going to help them out by posting Kristina's comment below as a main posting. Please read the posting and respond with either:

1. "Friday after school at school" or
2. "Saturday at 2 p.m. at Barnes and Noble".

hey guys kristina here.....well Leo and I were talkin today in PE while reciting our conjectures lol ::smiles at leo:: we were thinking the solution to this whole study session thing could be that we meet every first and thrid friday or saturday of every month at barnes and nobles at 2:00 pm....

NOW TO MY FELLOW GEOMETRY HONORS PEERS ALL YOU HAVE TO DO IS POST EITHER "friday" or "saturday" on which day you would like to meet....this is very easy...please dont make it any harder.....man i am startin to sound like ms.chan...lol....love you ms.chan and i am going to keep my promise...anyways back to topic please submit a vote (tolls closing at midnight). i will tally up the votes and we will have come to a conclusion.....i will announce the results tomorrow on the blog.....and it will come into motion MARCH of 2006...

thank you very much....kristina from first hour. good luck with homework tonight

Tonight's homework is just below this post......

Keep scrolling down for #4.3-#4.5 homework.

Midpoint, Slope, Parallel & Perpendicular Lines, & Equations of Lines

# 4.3

• (2-32) even
• (35-37) all

# 4.4

• (2-18) even

# 4.5

• (2-34) even

Post a question or a solution! Thanks!

Angle Relationships & Properties of Parallel Lines

# 4.1

• (1-17) all

# 4.2

• Investigation 4.2.1: If 2 parallel lines are cut by a transversal, then CA are ?, AIA are ?, AEA are ?, SSIA are ?, SSEA are ?
• Investigation 4.2.2: If 2 lines are cut by a transversal to form pairs of congruent CA, AIA, or AEA, then the lines are ?
• Investigation 4.2.3: Follow the instructions to construct a pair of parallel lines using the AIA or AEA method.
• (1-9 all, 13, 16, 18, 19)

Don't forget to begin working on the Construction Book. Samara from 3rd hour says that there is a study group at Barnes and Noble on Sunday (2 pm I think). Get on the blog and ask to be sure though. Other than that, I hope everyone has a very nice PG-13 weekend! See y'all Tuesday! :o)

Angle Relationships & Properties of Parallel Lines

# 4.1

• (1-17) all

# 4.2

• Investigation 4.2.1: If 2 parallel lines are cut by a transversal, then CA are ?, AIA are ?, AEA are ?, SSIA are ?, SSEA are ?
• Investigation 4.2.2: If 2 lines are cut by a transversal to form pairs of congruent CA, AIA, or AEA, then the lines are ?
• Investigation 4.2.3: Follow the instructions to construct a pair of parallel lines using the AIA or AEA method.
• (1-9 all, 13, 16, 18, 19)

Don't forget to begin working on the Construction Book. Samara from 3rd hour says that there is a study group at Barnes and Noble on Sunday (2 pm I think). Get on the blog and ask to be sure though. Other than that, I hope everyone has a very nice PG-13 weekend! See y'all Tuesday! :o)

Create a Construction Book

# 3.8

• (1-6, 10-13)

Construction Book Project

due date: February 24, 2006

NO LATE PROJECTS will be accepted.

NO EXCUSES!

Your job is to create a construction book that outlines in very specific directions how to perform the following constructions. Your instructions should be so detailed that a complete novice could follow your instructions and not have any problems doing the constructions below.

Your Construction Book must include:

1. cover page
2. table of contents
3. typed step-by-step instructions
4. one construction per side done by hand
5. may use front and backs of paper

Be creative with this.

Pick up a book that you've read and see what else you could add to your Construction Book if you were trying to sell it. Use Color! Remember that appearance is everything. That means neatness counts. You are competing with everyone else from both 1st and 3rd hours. So, the better your book is compared to others, the better your grade will be. I know we say that we shouldn't judge a book by its cover, but the truth of the matter is that we do judge a book by its cover all of the time. Your Construction Book should include the following constructions:

How to:

1. duplicate a segment
2. duplicate an angle
3. bisect a segment
4. bisect an angle
5. construct a perpendicular through a point NOT on a line
6. construct a perpendicular through a point ON a line
7. construct parallel lines using the rhombus method
8. parallel lines using the equidistant method
9. construct a 60 degree angle (equilateral triangle)
10. construct the incenter of a triangle
11. construct the circumcenter of a triangle
12. construct the orthocenter of a triangle
13. construct the centroid of a triangle
14. construct an inscribed circle of a triangle
15. construct a circumscribed circle of a triangle
16. construct the Euler Line

Take Home Construction Test

Complete your Construction Test. Please understand that the only reason why I am allowing you to take it home is because I NEED you guys to KNOW how to perform all of these constructions like the back of your hands. If you are not 100% proficient at these constructions, you will be setting yourselves for future failure. I don't care if you use your notes, book, computer, friends, whatever---to learn how to perform these constructions. Just know them. You are NOT, however, allowed to have someone else do the constructions for you. With that being said, write the following statement at the bottom of box # 19:

"I hereby declare that I, and I alone, have performed the previous constructions. If Ms. Chan finds out otherwise, I will receive an "F" as my grade." Please provide your signature, otherwise you will receive an "F" as a grade.

Prepare for Battle.....

Remember---- "The" Construction Test is tomorrow!

Practice doing your basic constructions:

1. duplicating a line segment
2. duplicating an angle
3. bisecting a line segment
4. bisecting an angle
5. perpendicular through a point NOT on a line
6. perpendicular through a point ON a line
7. parallel line using the rhombus method
8. parallel line using the equidistant method
9. equilateral triangle

Once you have those down pat, use your knowledge to construct various things such as the centers (incenter, orthocenter, centroid, circumcenter) of a triangle. Practice inscribing a circle within a triangle as well as circumscribing a circle about a triangle. Know how to construct a square with a given perimeter. Know how to construct various angles such as a 30 degree angle or a 22 and half degree angle. Know how to duplicate angles and segments in order to form a triangle. Basically, you MUST know EVERYTHING!

Euler Line

Since very few students were able to determine which 3 of the 4 centers of a triangle are collinear, you are to do it again for homework. You are to draw a large scalene triangle. Construct the incenter, circumcenter, orthocenter, and centroid of the triangle. 3 of the 4 centers will lie in a straight line. Remember, draw a SCALENE triangle.

If you are havinga difficult time because of all the arcs and lines surrounding this construction, perhaps you might want to invest some money in purchasing transparencies and overhead projection markers. Then, you could draw the same triangle on 4 transparencies. On transparency #1, construct the incenter. On transparency #2, construct the circumcenter. On transparency #3, construct the orthocenter. On transparency #4, construct the centroid. Then lie all 4 transparencies on top of one another and hopefully you'll be able to determine which 3 of the 4 centers of a triangle are collinear.

Centers of a Triangle

New vocabulary words:

1. incenter- point of concurrency of 3 angle bisectors of a triangle
2. orthocenter - point of concurrency of 3 altitudes of a triangle
3. circumcenter - pt. of concurrency of 3 perpendicular bisectors of a triangle
4. centroid - point of concurrency of 3 medians of a triangle

I know I said I wouldn't do this, but I can't stand to watch some of you struggle. The following website may help those of you who are having a tough time with constructions. The sound may be choppy the first time.

Allow it to play all the way through and

then listen to it again.

It'll come out clear the second time you listen to it.

http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=construc

Your assignment this weekend is:

1. Construct the incenter of a large acute triangle.
2. Construct the incenter of a large obtuse triangle
3. Construct the inscribed circle of # 1 and # 2.
4. Construct the orthocenter of a large acute triangle.
5. Construct the orthocenter of a large obtuse triangle.
6. Construct the circumcenter of a large acute triangle.
7. Construct the circumcenter of a large obtuse triangle.
8. Construct the circumscribed circle of # 6 and #7.
9. Construct the centroid of a large acute triangle.
10. Construct the centroid of a large obtuse triangle.

Any questions? Post them here. Do you know constructions well? Post your steps here. Just a suggestion: form a study group at Barnes and Noble this weekend. Have a cafe mocha while performing constructions. Wahoooooo! Fun! Fun!

Construction Problems

Lucky you for checking the blog.....

I originally was going to assign # 3.6 AND # 3.7 for homework. However, I forgot that you have a Ch. 2 Test tomorrow so it doesn't make sense that I assign both # 3.6 and # 3.7 because there is no way we'll be able to discuss all of it given that 45 minutes of tomorrow's class will be devoted to you taking the test. SO..... # 3.6 (1-14) is all you have to do for homework. I repeat:

# 3.6

• (1-14) all

Please post a question or a solution. Love ya! Happy constructing! :o)

Constructing Angle Bisectors and Parallel Lines

# 3.4

• (1-16) all---you must describe AND perform the constructions!

# 3.5

• (8-12) all

Post a question or a solution. I KNOW that some of you are LOST when it comes to doing constructions, so don't even front. Post a question and someone should come to your rescue. Remember---Neighbors helping neighbors!

Constructing Perpendicular Bisectors & Perpendiculars

# 3.2

• Complete conjecture from I 3.2.2
• (7-11) all
• (13-14)

# 3.3

• I 3.3.2
• don't forget to complete the conjecture!
• (1-6) all

Pick one: post a question or post a solution.

Duplicating Segments and Angles

# 3.1

• (1-10) all
• (12)

Post a question or comment!

Review your flashcards! There will be a quiz on Monday on every single vocabulary word in Ch.2! This includes those you defined in your investigations, as well as the bold-faced words.

# 2.9

• (1-12)
• (14-16, 23) all

Have a PG-13 weekend!

FLASHCARDS! FLASHCARDS!! FLASHCARDS!!!

# 2.8

• (1-6) all
• (12-35) all

# 2.9

• READ pgs. 120-123
• (10-12)
• we will be doing 14-23 in class tomorrow so if you want to get them copied now, you'll be ahead of the game

Don't forget to post a question or a solution!!!! I know some of those true/false questions are difficult so don't even play!

# 2.8

• read pgs. 111-112
• (1-6) all
• (12-35) all

Don't forget to make flashcards of ALL vocabulary words!