Chapter 7 Review

Today we reviewed Chapter 7 and some of Chapters 1-6.  Tomorrow we will review further.  For Chapter 7, you should know how to:

• Use the Pythagorean Theorem to Solve for the Missing Side of a Right Triangle
• Find the Area of an Isosceles Triangle, given its side lengths
• Use the Converse of the Pythagorean Theorem to Classify A Triangle as Acute, Right, or Obtuse
• Solve for missing sides of Similar Right Triangles by either setting up corresponding proportions or by using the Geometric Mean (Leg) Theorem or the Geometric Mean (Altitude) Theorem
• Know the Properties of Special Right Triangles and know how to simplify answers in simplest radical form
• Know how to apply sine, cosine, and tangent ratios to solve missing sides of a right triangle
• Know how to apply inverse sine, cosine, and tangent ratios to solve missing angles of a right triangle.

For homework, please complete the Chapter 7 Test on Page 498 #1-17 ALL problems.  Also, please complete the Chapter 7 Study Project.  You have a Cumulative Test on Chapters 1-7 on Thursday.
The Chapter 7 Study Terms include:

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

Inverse Trigonometric Ratios

7.7 Inverse Trig Ratios

Today we learned how to use the inverse trig ratios to help us solve right triangles.  To solve a right triangle means to solve for all missing angles and side lengths.

Tonight's homework is P. 485-486 #5,7,9,13,29

(sorry for the late post!)

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