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