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