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