7.6- Sine and Cosine Ratios

Today we looked at the other two trigonometric ratios: sine and cosine ratios.  These three ratios (along with tangent) can help you find the length of a missing side of a right triangle.  After break we will look at how to solve for missing angle measures as well.

Tonight's homework is P. 477-478 #5,9,16,18,19, and 29.

Try this animation on angles of depression for an application of the sine and cosine ratios.
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch07_pg475.html

7.5- Tangent Ratio

Today we began looking at trigonometric ratios, specifically the tangent ratio.

Tonight's homework is P. 469-470 #5,7,16,17,21, and 25

Please see this video to help you understand the tangent ratio better:
http://www.brightstorm.com/math/geometry/basic-trigonometry/trigonometric-ratios-tangent

7.4- Special Right Triangles

Today we talked about two special right triangles that have properties to help you solve for the side lengths of the triangles.  These triangles are the 45-45-90 and 30-60-90 triangles.

Tonight's homework is P. 461-462 #5,6,9,13,18,19,and 29

Check out this animation to help you with Special Right Triangles:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch07_pg460.html

Chapter 7 Study Project Continued...

Today we finished up our discussion on the Geometric Mean (Altitude) Theorem and the Geometric Mean (Leg) Theorem used in Similar Right Triangles.  Over the weekend, please work on the following terms of your study project:

Geometric Mean
Similar Right Triangles Theorem
Geometric Mean (Altitude) Theorem
Geometric Mean (Leg) Theorem

Enjoy the weekend!  =)

7.3- Similar Right Triangles

Today we talked about how similar right triangles are formed when an altitude is drawn from the right angle of a right triangle.  The Geometric Mean (Altitude) and The Geometric Mean (Leg) Theorems are good shortcuts to remember when solving for missing sides of these right triangles.

Tonight's homework is P. 453-454 #5,9,15,19,20,21
Check out this animation to help you understand how geometric means are used in right triangles: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/9_1.html

7.3- Similar Right Triangles Investigation and Ch. 7 Study Project

Today we did an investigation of Similar Right Triangles.  We will continue learning about the relationship between the 3 right triangles formed by an altitude drawn from a right angle of a right triangle.  For homework, please complete the first four study terms of the Chapter 7 Study Project

Ch. 7 (13)

Pythagorean Theorem

Converse of the Pythagorean Theorem

Classifying Acute Triangles Theorem

Classifying Obtuse Triangles Theorem

Geometric Mean

Similar Right Triangles Theorem

Geometric Mean (Altitude) Theorem

Geometric Mean (Leg) Theorem

45-45-90 Triangle Theorem

30-60-90 Triangle Theorem

Tangent Ratio

Sine Ratio

Cosine Ratio

7.2- Converse of the Pythagorean

Today we learned how to classify triangles by angles when we know the lengths of the sides of the triangles.  Using the converse of the Pythagorean Theorem, we can determine if a triangle is a right triangle, an obtuse triangle or an acute triangle.

Tonight's homework is P. 444-445 #3,7,11,13,17,21,24, and 25

For extra practice, please see the Section 7.2 Practice found here:
http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html

7.1- Pythagorean Theorem

Today we begin our chapter on Right Triangles, the last chapter on Triangles.  We are half way through the material and I am proud of all we have accomplished so far this year.  Today we discussed the Pythagorean Theorem and applied it to finding the area of an isosceles triangle.

Tonight's homework is P. 436-438 #5,11,17,21,23, and 27

Check out this animation that's helps you visual a proof of the Pythagorean Theorem:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch07_pg434.html

Chapter 6 Review and Study Project

Today we reviewed the Chapter 6 Study Project terms.  Please complete the study project by tomorrow in preparation for your Chapter 6 quiz that will be given tomorrow.  See the terms below:

Ch. 6 (8)

Similar Polygons

Scale Factor

AA Similarity Postulate

SSS Similarity Postulate

SAS Similarity Postulate

Triangle Proportionality Theorem (including converse)

Parallel Lines Proportionality Theorem

Angle Bisectors and Opposite Ratios Theorem

Also, you may review vocabulary by completing this crossword puzzle:

http://www.classzone.com/cz/books/geometry_2007_na/crossword.htm?id=xword_ch6

6.6- Use Proportionality Theorems

When dealing with similar polygons, we see a lot of proportions that are formed.  Today we discussed Triangle Proportionality Theorem, Parallel Lines Proportionality Theorem, and the Angle Bisector and Opposite Ratio Theorem.

Tonight's homework is P. 400-401 #5,8,9,13,15, and 16.  Please bring either flashcards or your notebook to work on a new study project tomorrow in class.

For some challenging bonus material, check out this animation on fractals and how they use Proportionality Theorems:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch06_pg407.html
For more help on proportionality theorems, please watch these videos:
http://www.brightstorm.com/math/geometry/similarity/proportional-segments-between-parallel-lines
http://www.brightstorm.com/math/geometry/similarity/angle-bisectors-and-opposite-side-ratios

6.5- SSS and SAS Similarity Theorems

Today we discussed the final two shortcuts to prove that triangles are similar to each other.  The three ways that you can prove that triangles are similar are the Angle-Angle (AA) Similarity Postulate, the Side-Side-Side (SSS) Similarity Theorem, and the Side-Angle-Side (SAS) Similarity Theorem.

Tonight's homework is P. 392-393 #5,7,11,14,19, and 21
Also, please remember that the FINAL DAY to turn in test corrections is TOMORROW.

Here is a video that teaches about the similarity shortcuts in case you are still confused:
http://www.brightstorm.com/math/geometry/similarity/similarity-shortcuts
Here are some animations to help you determine if triangles are smiliar:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch06_pg391.html
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch06_pg394.html

6.4- AA Similarity Postulate

Today we learned about the properties of similar polygons, and the first way to prove that two triangles are similar (Angle-Angle Similarity Postulate).  We also spent some time going over commonly missed questions on the test.

Tonight's homework is P. 384-385 #9,13,16,20, and 23.  Also, please complete the test corrections and return NO LATER THAN TUESDAY due to the end of the marking period.  Remember that you can receive up to half of the points that you lost if you complete the test corrections properly.
The format for test corrections is:

• Question
• Incorrect Answer
• Correct Answer with work shown
• Reason you got your answer incorrect (be specific)

Have a great weekend!!

Preparing for Chapters 1-5 Test

To study for tomorrow's test, please try the practice test found here for Chapter 5: http://www.classzone.com/etest/viewTestPractice.htm?testId=21154
AND, try practice problems from all of the previous tests:
http://www.classzone.com/cz/books/geometry_2007_na/page_build.htm?id=resources/applications/oltp/ny/online_test_practice&qtype=chapter

Also, check out these helpful videos on any topics you are still having trouble with:
http://www.brightstorm.com/math/geometry/triangles
http://www.brightstorm.com/math/geometry/constructions

Chapter 5 Review

Today we reviewed about segments in a triangle, including perpendicular bisectors, angle bisectors, medians, and altitudes and their theorems associated with them.

For homework please complete the Chapter 5 Test in your textbook, P. 348 #1-18 ALL while studying for your cumulative test on chapters 1-5 on Thursday and
The Chapter 5 Study Project is due tomorrow and should include all of the following terms:

Midsegment

Midsegment Theorem

Perpendicular Bisector

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector Theorem

Concurrency of Perpendicular Bisectors of a Triangle Theorem/Circumcenter

Angle Bisector

Angle Bisector Theorem

Converse of the Angle Bisector Theorem

Concurrency of Angle Bisectors of a Triangle Theorem/Incenter

Median

Concurrency of Medians of a Triangle Theorem/Centroid

Altitude

Concurrency of Altitudes of a Triangle Theorem/Orthocenter

Triangle Inequality Theorem

Hinge Theorem

Converse of the Hinge Theorem

5.6- Hinge Theorem

Today we compared inequalities in two different triangles by using the hinge theorem.

Tonight's homework is P. 338-340 #5,7,9,17, and 24
Also, please remember that the Chapter 5 study project is due on Wednesday 12/1 and we have a test on Thursday, 12/2 covering everything since the beginning of the year Chapters 1-5, constructions, and linear-quadratic equations.

Check out this animation to help you understand the hinge theorem: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch05_pg336.html

5.5- Inequalities in a Triangle

Today we looked at the Triangle Inequality Theorem and how the sides and angles related to each other in a triangle.

Tonight's homework is P. 331-332 #9,12,17,19,20,21,25, and 33

Your Chapter 5 Study Project is due on Wednesday 12/1

Please check out these videos to help you understand today's lesson:
http://www.brightstorm.com/math/geometry/triangles/triangle-side-inequalities
http://www.brightstorm.com/math/geometry/triangles/triangle-side-and-angle-inequalities

Happy Thanksgiving!  Enjoy the long weekend!  =)

8th Grade State Test Diagnostic

Today we took a diagnostic of the 8th Grade State Test Material.  Please complete the Free Response packet for homework.  If you were absent, you can download it at the following two websites:
http://www.nysedregents.org/Grade8/Mathematics/20080306book2.pdf
http://www.nysedregents.org/Grade8/Mathematics/20080306book3.pdf

5.4- Use Altitudes of a Triangle

Today we learned how to find the orthocenter of a triangle.  The orthocenter is the point of concurrency of altitudes of a triangle.

This weekend's homework is P. 323 #17-22, and 29-31.  Also, we will have a quiz on 5.1-5.4 on Monday.  Please review the Study Project terms through "orthocenter" and be sure you know the properties of segments in a triangle.  If you were absent today, please email me for the list of terms you are responsible for knowing by Monday.

Please the following animation to help you understand orthocenters: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch05_pg321.html

5.4- Use Medians of a Triangle

Today we investigate the lengths of medians in a triangle and investigated how they are related to each other when they intersect.  Please be sure to know the Concurrency of Medians of a Triangle theorem.  If you were absent, please try the activity on Page 318 of your textbook to help you understand the theorem.

Tonight's homework is P. 322-323 #5,7,9,25,27, 33

5.3- Angle Bisectors in a Triangle

Today in class we investigated angle bisectors and their relationship to triangles.  Please make sure you know the Angle Bisector Theorem and its converse as well as the Concurrency of Angle Bisectors (Incenter) Theorem.

Tonight's homework is P. 313-314 #3,5,7,13,19,23,25

Please visit the animation on the concurrency of angle bisectors:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch05_pg312.html

5.2- Perpendicular Bisectors of a Triangle

Today we investigated perpendicular bisectors and how they are related to triangles.  Make sure that you know how to use the Perpendicular Bisector Theorem and its converse as well as know the Concurrency of Perpendicular Triangles Theorem

Tonight's homework is P. 306-308 #3-15 ODDS, 16, 17

Check out this animation to learn more about perpendicular bisectors:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch05_pg304.html

5.1- Midsegment of a Triangle

Today we did an investigated the relationship between the midsegment of a triangle and the sides of the triangle.  Please go over the investigation and review the results to conclude some facts about midsegments of a triangle.  If you didn't copy it down in class, please copy down the Midsegment Theorem in your textbook.

Tonight's homework is P. 298-299 #3,5,9,11,25,37

Try these problems for practice with midsegments of a triangle: http://www.regentsprep.org/regents/math/geometry/GP10/PracMid.htm

4.7- Isoscles and Equilateral Triangles

Today we learned about properties of Isosceles and Equilateral Triangles using the Base Angle Theorem and the Converse of the Base Angle Theorem.

Tonight's homework is P. 267-268 #5,12,17,19,21, and 23.  There will be a quiz on Chapter 4 on Friday (not cummulative).  Also, your study project for Chapter 4 is due on Friday as well.

Try this crossword puzzle to see if you know all of the vocabulary from Chapter 4.
http://www.classzone.com/cz/books/geometry_2007_na/crossword.htm?id=xword_ch4
Try this chapter test also for more practice on these concepts:
http://www.classzone.com/etest/viewTestPractice.htm?testId=4683

4.6- CPCTC

Today we discussed how to apply CPCTC which stands for Corresponding Parts of Congruent Triangles are Congruent.  Once you have proven that two triangles are congruent, the corresponding parts must also be congruent.  We also went over the chapter 4 terms you must have for your study project, which is due on Friday.

The Chapter 4 Study Project terms are:

Triangle Sum Theorem

Exterior Angle Theorem

Third Angles Theorem

SSS Congruence Postulate

SAS Congruence Postulate

HL Congruence Theorem

ASA Congruence Postulate

AAS Congruence Theorem

CPCTC

Base Angles Theorem

Converse of Base Angles Theorem

Tonight's homework is P. 259-261 #11,14,23,26,31.  Please remember that your Chapter 4 QUIZ is on Friday and the corresponding study project is due that day also.

For additional help, please see the video on CPCTC:

http://www.brightstorm.com/math/geometry/triangles/cpctc

For more help on flow proofs, see this animation:

http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/3_2.html

4.5- ASA and AAS

Today we learned the final to ways to prove that triangles are congruent: Angle-Side-Angle (ASA) Congruence Postulate and Angle-Angle-Side (AAS) Congruence Theorem.  We will be continuing to practice writing proofs using all the different triangle congruence shortcuts that we have learned.

Tonight's UPDATED homework is P. 252-254 #5,9,13,15,25, and 33
We will also have a Chapter 4 Quiz on Friday.

If you were absent, please see the video on ASA and AAS: http://www.brightstorm.com/math/geometry/triangles/asa-and-aas
Visit the section 4.5 eworkbook for more problems on classzone:
http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html

4.4- SAS and HL

Today we talked about two more shortcuts to prove that triangles are congruent- SAS (Side-Angle-Side) Congruence Postulate and the HL (Hypotenuse-Leg) Congruence Theorem.  We also discussed why there is no such thing as the SSA (Side-Side-Angle) Congruence Postulate/Theorem.

Tonight's homework is P. 243-245 #13,15,31,34, and 35

Please see the following videos for additional explanation of the theorems if you are still confused:
http://www.brightstorm.com/math/geometry/triangles/sss-and-sas
http://www.brightstorm.com/math/geometry/triangles/hl
http://www.brightstorm.com/math/geometry/triangles/why-ssa-and-aaa-dont-work-as-congruence-shortcuts

4.3- SSS Congruence Postulate

Today we learned the first method of proving that triangles are congruent- the Side-Side-Side (SSS) Congruence Postulate.

Tonight's homework is P. 236- 238 #6,9,16,17, and 25.  Also, you received your test #2 back today and you should work on your test corrections and get your parent signature by FRIDAY.

4.2- Congruent Figures

Today we learned about the properties of congruent figures and we proved the Third Angle Theorem.  Please review the textbook for this section if you were absent.

Tonight's homework is P. 228-231 #3,8,9,13,15,19,21,28,33, and 34

Check out section 4.2 in the online eworkbook for extra practice problems: http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html

4.1- Apply Triangle Sum Properties

Today we began our unit on triangles.  Today we learned about the Triangle Sum Theorem and the Exterior Angles Theorem.

This weekend's homework is P. 221-222 #9,12,15,18,31,33,35.

Have a great weekend and Happy Halloween!

Chapter 1-3 Cumulative Test Tomorrow!

Tomorrow if your Cumulative Test.  It includes everything that we have learned since the beginning of the year.  Specifically, you should know these topics:

• Everything from the first test: http://nest8thgrademath2010.blogspot.com/2010/10/unit-1-and-2-test-review.html
• Quadratic-Linear Systems of Equations
• Parallel Lines
• Angle Pair Relationships (Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles)
• Slopes of Parallel Lines Postulate
• Writing and Graphing Equations of Parallel Lines
• Perpendicular Lines
• Slopes of Perpendicular Lines Postulate
• Writing and Graphing Equations of Perpendicular Lines
• Lines Perpendicular to a Transversal and Perpendicular Transversal Theorems
• Constructions (the new ones are Parallel Lines through a point, Perpendicular Lines through a point, and Equilateral Traingle)

Please complete the handout from class for practice.  Also, visit the following website for a crossword puzzle on Chapter 3 vocabulary: http://www.classzone.com/cz/books/geometry_2007_na/crossword.htm?id=xword_ch3

Quadratic-Linear Systems of Equations

Today we did an investigation on solving quadratic-linear systems of equations and the types of solutions you can have.  The homework is a worksheet that we passed out in class.  If you were absent, please see me tomorrow for a copy of the homework as well as the investigation we did in class.

Please remember that your Chapter 3 study guide is due tomorrow in preparation for our Test on Chapters 1-3 on Thursday.  Tomorrow we will be reviewing for the test.

Solving and Graphing Quadratic Equations

Today we reviewed solving and graphing a quadratic equation.  Even though you learned this in algebra, you are also responsible for knowing it for both the 8th grade State Test and Geometry Regents so it is important that we review this material.  I have linked a few videos to help you if you are still lost after today's lesson.  Tomorrow we will be solving quadratic-linear systems by graphing.

In class we solved and graphed the equation x^2 - 11x + 30 = 0
For homework, please graph the equation 2x^2 + 5x - 12 = y which we solved in class.  Only use a graphing calculator to check your work.

For a review of factoring, please visit:
http://www.brightstorm.com/math/algebra/factoring-2/factoring-trinomials-a-equals-1
http://www.brightstorm.com/math/algebra/factoring-2/factoring-trinomials-a-is-not-1
For a review of graphing quadratic equations, please visit:
http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/graphing-quadratic-equations

3.6- Prove Theorems about Perpendicular Lines

Today we learned and proved theorems relating to perpendicular lines.

Tonight's homework is P. 194-197 #8, 15-17, 21, 31
Also, please know that your Geometric Construction book is due tomorrow.  The FINAL DAY to turn this in to receive credit for this marking period (which ends tomorrow) is Monday.

Chapter 3 of your study project is due next Wednesday.  Please see the list of terms at the previous post called "Study Project Chapter 3" found here: http://nest8thgrademath2010.blogspot.com/2010/10/study-project-chapter-3.html  Your cumulative Chapter 1-3 test will be next Wednesday as well.

3.5- Writing and Graphing Equations of Lines

Today we learned how to write and graph equations of lines in slope-intercept form and standard form.  We specifically learned how to write and graph equations of lines parallel and perpendicular to given equations and through a given point. 

Tonight's homework is P. 184-187 #4,8,9,11,14,17,23,26,31,34

Also, please remember that the final product of your Geometric Construction Book is due on Friday.

Please see this animation to explore a comparison of lines http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/explore_learning/chapter_3/dswmedia/Alg1_4_6_Slope_I.html

Construction Book Part 2

Today we went over the rest of our constructions for our Construction Book Project.  The final product of our book is due on Friday.
Your book should include a cover page, table of contents, the previous constructions and new constructions:

• Copy a segment
• Bisect a segment
• Copy an angle
• Bisect an angle
• Line Parallel to a given line through a given point
• Line perpendicular to a given line through a given point
• Equilateral Triangle

Please visit this website for videos that will help you with your constructions:

http://www.brightstorm.com/math/geometry/constructions/constructing-a-perpendicular-to-a-line

http://www.brightstorm.com/math/geometry/constructions/constructing-parallel-lines

3.4- Slopes of Lines

Today we learned how to compare slopes of lines.  Please be sure you know the Slopes of Parallel Lines Theorem and the Slopes of Perpendicular Lines Theorem.

This weekend's homework is P. 175-176 #3-6, 13, 15, 16, 18, 23, and 25.  Also, we have a quiz on sections 3.1-3.4 on Monday.  Have a good weekend!

For more information on comparing slopes of lines, check out this animation: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch03_pg174.html

Study Project Chapter 3

For your reference, please see the following terms for Chapter 3 that will be included in your study project.  Please only begin working on the terms we have completed in class.  The due date for this part of the project will be Wednesday, October 27. 

Ch. 3

Parallel Lines

Transversal

Corresponding Angles (Include Corresponding Angles Postulate and Corresponding Angles Converse)

Alternate Interior Angles (Include Alternate Interior Angles Theorem and Alternate Interior Angles Converse)

Alternate Exterior Angles (Include Alternate Exterior Angles Theorem and Alternate Exterior Angles Converse)

Consecutive Interior Angles (Include Consecutive Interior Angles Theorem and Consecutive Interior Converse)

Slopes of Parallel Lines Postulate

Slopes of Perpendicular Lines Postulate

Perpendicular Transversal Theorem

Lines Perpendicular to a Transversal Theorem

Standard Equation of a Line

Slope-Intercept Form of a Line

Point-Slope Form of a Line

3.3- Proving Lines Parallel

Today we used the converse of the corresponding angles postulate, alternate interior angles theorem, alternate exterior angles theorem, and consecutive interior angles to prove when lines are parallel.

Tonight's homework is P. 165-169 #4, 7, 11, 14, 23, 31, 46, and 47.  Also please remember that Test Corrections and Parent Signature for your Unit 1 and 2 Test are due tomorrow.

For extra problems on today's lesson, please visit section 3.3 on the eworkbook:
http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html

3.2- Angle pairs related to Parallel Lines

Today we discussed the angle pair relationships of parallel lines.  Please make sure you know the Corresponding Angles Postulate, Alternate Exterior Angles Theorem, Alternate Interior Angles Theorem, and the Consecutive Interior Angles Theorem.  (You have to know the names of these types of angle pairs!!)

Tonight's homework is P. 157-160 #3, 9-16, 23, 29, 32, 33, 41, 44-46.  Also, your test corrections and Parent Signature for your Unit 1 and 2 Test are due on Thursday.  Since you have two days to complete this, I suggest that you begin working on Test Corrections to complete it in case you have a lot to correct.

Check out this section's animation!! http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch03_pg155.html

3.1- Identify Pairs of Lines and Angles

Today we learned what parallel and skew lines are and discovered the names of the angle pairs formed by a transversal intersecting two coplanar lines.  Please be sure you can identify corresponding, alternate interior, alternate exterior, and consecutive interior angles by Tuesday.

This weekend's homework is P. 150-152 #3-6, 11-14, 18-23, 28, 45, and 46

Check out this animation to help you understand parallel and perpendicular lines better.  http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch03_pg148.html

Have a great 3-day weekend!

Unit 1 and 2 Test Review

Today we finished reviewing for our Unit 1 and 2 Test tomorrow.  Please note the following:

• The test will include regents questions in both multiple choice and short answer forms.
• You will have the class time to finish and no longer unless if you receive official testing modifications.
• If I did not grade your study project today in class, you must have it available for me to check during the test tomorrow.  

Test topics that you are responsible for knowing are:

• Midpoint Formula
• Distance Formula
• Complementary, Supplementary, and Vertical Angles
• Linear Pairs
• Conditional Statements (If-Then Form, Inverse, Converse, Contrapositive, and Biconditional)
• Points, Lines, and Planes Postulates
• Classifying polygons
• Segment Theorems and Postulates
• Angle Theorems and Postulates
• Congruency
• Two-column Proofs
• Constructions

Geometry Study Project

Today we discussed the requirements of your Geometry Study Project.  Please see below for the handout received in class.  Please complete Chapters 1 and 2 by Wednesday.  Your first Test (on Chapters 1 and 2) is on Thursday.  Let me know if you have any questions.

Geometry Study Project

You have the option of creating flashcards, a study notebook, or study sheets by chapter.  At the end of each chapter, you will create your choice based on the required vocabulary and facts from each chapter that you are responsible for knowing.  You should include examples when necessary.  After each chapter, you will receive a grade on organization and completeness of your study materials.

Flashcards: Designed to have you test yourself or with a partner key vocabulary and facts about geometry.

Study Notebook: Designed for those students who prefer to study from a notebook, but this should be separate from your class notebook.

Study Sheets: For those who like to look at one page to get all of your important facts, you can choose this option for each chapter, or you can include multiple chapters on one sheet if it fits.

Required Geometry Vocabulary and Facts

Ch. 1:

Midpoint Formula

Distance Formula

Segment Addition Postulate

Angle Addition Postulate

Definiton of Congruency (ie. Congruent Segments, Congruent Angles)

Complementary Angles

Supplementary Angles

Regular Polygon

Ch. 2:

Counterexample

If-Then Form of a Conditional Statement

Converse of a Conditional Statement

Inverse of a Conditional Statement

Contrapositive of a Conditional Statement

Biconditional Statement

Perpendicular Lines

Substitution Property

Distributive Property

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Congruence of Segments Theorem

Congruence of Angles Theorem

Right Angles Congruence Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

Linear Pair Postulate

Vertical Angles Congruence Theorem

Two-Column Proof

2.7- Angle Pair Relationships

Today we learned and proved different angle pair relationships.  You should know the Right Angles Congruence theorem, the Congruent Supplements Theorem, the Congruent Complements Theorem, the Linear Pair Postulate, and the Vertical Angle Congruence Theorem.

Tonight's homework is P. 127-131 #3,4,11,13,16,29,37,49, and 50

Please visit the @HomeTutor for extra help with this lesson which includes a mini-lesson and extra practice problems: http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/athometutor/media/ii.html?chapter=2&lesson=7&state=NY

2.6- Prove Statements about Segments and Angles

Today we began writing proofs about the congruency of segments and angles.  Please remember that writing proofs takes practice because forming a logical argument does not always come easily to many of us.  Do not discouraged, and know that we will be writing many proofs about many geometric concepts throughout the year.

Tonight's homework is P. 116-119 #4, 12, 16, 17, 18, 22, 31

Please try the animation for more practice: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch02_pg119.html

2.5- Reason using Algebraic Properties

Today we learned how to use Algebraic Properties to apply deductive reasoning to form logical arguments.  We learned the Addition Property, Subtraction Property, Multiplication Property, Division Property, Substitution Property, Distributive Property, Reflexive Property, Symmetric Property, and the Transitive Property.  Please practice these properties because we will use them throughout the school year.

Tonight's homework is P.109-111 5,9,14,17,21-25,33,39 and we have a QUIZ tomorrow on sections 2.1, 2.2, 2.4, and 2.5 in the textbook.

Please do practice 2.5 in the eworkbook http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html
and do the section quizzes to prepare for the quiz tomorrow.
http://www.classzone.com/cz/books/geometry_2007_na/page_build.htm?id=resources/applications/oltp/ny/online_test_practice&qtype=section

2.4- Use Postulates and Diagrams

Today we learned about how to apply postulates about point, lines, and planes to interpret and sketch diagrams.

Tonight's homework is P. 99-102 #3,4, 6-24 all, 46, and 47

Please visit Section 2.4 in the eworkbook for more practice: http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html

Your next quiz will be on Sections 2.1, 2.2, 2.4, and 2.5 on Wednesday, September 29.

2.2- Analyzing Conditional Statements

Today we learned about conditional statements, including the converse, inverse, and contrapositive of a statement and whether or not it can be written as a biconditional statement.  These concepts will be reviewed throughout the year and applied to theorems and definitions and proofs that we will learn in Geometry this year.

This weekend's homework is P. 82-85 #3-15 odds, and 19-27 odds.  Also, your Geometric Construction Book Part 1 is due on Monday.  Please review the directions and look at P. 33-34 in your textbook for further help with creating the required constructions.

Please use this animation to help you analyze conditional statements: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/2_1_2.html

2.1- Inductive Reasoning

Today we described patterns and made conjectures using inductive reasoning.

Tonight's homework is P. 75-78 #7,13,15,21,29,39,40

Visit the animation for this lesson for more information: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/g7_1_1.html

1.7- Perimeter and Area of Polygons and Circles

Please review the formulas for area and perimeter of rectangles, triangles, and circles.  Today, we applied the distance formula to find the perimeter of polygons.

Tonight's homework is P. 52-55 #5,7,13,17,19,21,25,31,35.

For extra help with today's lesson, please use the @Home Tutor for the lesson: http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/athometutor/media/lessonmenu.html?chapter=1&lesson=7&state=NY
Please review chapter one vocabulary, by using the flashcards found here: http://www.classzone.com/cz/books/geometry_2007_na/get_chapter_group.htm?cin=1&ci=1&rg=games_and_activities&at=math_Vocabulary_flipcards&var=math_vocabulary_flipcards
Then complete this crossword puzzle: http://www.classzone.com/cz/books/geometry_2007_na/crossword.htm?id=xword_ch1

Geometric Construction Book Part 1

Today we learned about our Geometric Construction Book Project.  We learned how to do the first four constructions: copy a segment, bisect a segment, copy an angle, and bisect an angle.  Please know that for you book, you need to draw the construction and write detailed step-by-step instructions on how you made the construction.  For help, you can see P. 33-34 in your textbook.  The first part of the construction book is due on Monday, September 27, 2010.

1.6- Classifying Polygons

Today we reviewed/learned different ways to classify polygons.  Please be sure you know what a polygon is, how to name them, the difference between convex and concave polygons, equilateral, equiangular, and regular polygons.

Tonight's homework is P. 44-45 #3, 5, 7, 11, 13, 17, 29, and 37

Check out this PacMan animation to practice classifying polygons http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/6_1.html

1.4 and 1.5 Angle Classification and Angle Relationships

Today we reviewed various angle classifications (acute, obtuse, right, straight) and learned new angle relationships (congruent, complementary, supplementary, linear pairs, and vertical angles).  These are fundamental to geometry and we will continue using these throughout this year.

This weekend's homework is P. 29-30 #21-47 odds only, AND P. 39-40 #9-42, every 3rd problem (ie.9,12,15,18, etc).

If you do not know how to use a protractor or need a review, please visit this animation: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/g6_9_2.html

1.3- Midpoint and Distance Formulas

Today we investigated how to find the midpoint and length (distance) of a segment given its endpoints.  Please recall the use of averages and the pythagoren theorem when using the formulas.

You homework is P. 19-22 #3-48, every third problem (ie. 3,6,9,12, etc.) and problems 55-57 on the same page.

Visit the animation for more information: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch01_pg21.html
Also you can see section 1.3 problems here:
http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html
And quiz yourself for understanding!
http://www.classzone.com/etest/viewTestPractice.htm?testId=4479

1.2- Segment Congruency

Today we learned the difference between segment length equality and segment congruency.  Please be sure you understand that equality pertains to numerical measurements and congruency pertains to geometric figures.  Also, be sure to know the correct symbols and notations for each.  Please see the below resources for extra help.  Even though we did not go over it in class today, you are also expected to know how to use a ruler to take measurements of segment lengths.

Tonight's homework is P. 12-13 #1,8,10,16,19,24,26,33.  Remember to show work when applicable and be aware that homework is graded mainly on effort.  Copying or cheating benefits you in no way.  Understanding the concepts are infinitely more important than getting a good homework grade.  If for whatever reason you are unable to complete your homework on a given night, please just do it for homework the next night- do not copy someone's homework.  Help us to maintain the academic integrity of this course.

Visit this animation for extra practice on today's topic: http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/geom07_ch01_pg14.html
Also, you can visit section 1.2 workbook for more practice problems.  http://www.classzone.com/cz/books/geometry_2007_na/resources/htmls/ml_hsm_geom_eWorkbook/index.html
Want to see how you would do on a quiz on today's lesson? Take one here: http://www.classzone.com/etest/viewTestPractice.htm?testId=4479

Lesson 1.1- Points, Lines, and Planes

Today we learned the undefined terms of points, lines, and planes and did an investigation on the intersection of lines and planes.  Please make sure you know the correct way to NAME the various geometric figures that we learned today.

Your homework is to complete textbook P. 5-8 #1-22 ALL, and 28-38 EVENS.  Please sign up at our textbook website http://www.classzone.com/cz/books/geometry_2007_na/book_home.htm?state=ny if you haven't already done so to sign up for a student account.  Please use the activation code: 4966580-10 to access your online copy of our textbook.  Visit the animated math section and complete animation 1.1 for more practice on today's lesson!

Please remember that all math supplies should be brought into school tomorrow.  You may leave your index cards at home until I tell you when we will start using them.

Welcome and Syllabus

Hello my new 8th grade class!  Welcome to our Geometry blog, where you can check my daily post to find homework and anything I may have forgotten to mention in class that day.  Today you got your syllabus which you should go over with your parents and sign it and bring it back tomorrow.

Please note that on the syllabus, I posted important websites that you should visit frequently and whenever you need help in this course.  Please check this blog regularly and become familiar with how to find older posts (to the archive on the right, listed monthly).  Also, please visit our textbook website: http://www.classzone.com/cz/books/geometry_2007_na/get_center_home.htm?rg=quick_reference
Create a student account and enter the following activation code: 4966580-10 to access the online copy of our textbook.
For your reference, I have posted an additional website for your use of Regents prep: http://www.regentsprep.org/Regents/math/geometry/math-GEOMETRY.htm
Feel free to visit this site for additional help with anything Regents related.

If you have any questions, feel free to comment on this blog or send me an email at jberger6@schools.nyc.gov
Have a great first full week of school!