Geometry

On this page, I will be posting power points that deal with the topics we discuss in class. 

We discussed ideas on how to demonstrate good participation in class.  Based on student suggestions and a few points I found from other sources, here is the list:

Thinking:

Questions & Answers while Discussing the Topic

            Writing and Working Problems

            Concentration (Staying focused) and  Comparing Arguments with Other Students

Collaborating and Communicating

            Working in Groups

            Making sure everyone in the group understands and can explain the topic

            Comparing arguments

Justification

            Work to prove correct.

           Show all the details

            Able to give reasons

Representation

             Showed all work with clear labeling and organization.

            Understood the question clearly and showed it with diagrams

            Show multiple ways to the result

           Our work is clear enough for any person to understand it.

 

Chapter 1 - Points, Lines, Planes, and Angles (Sections 1 and 2)

Points, Lines, Planes

http://pdesas.org//EduPortal/Home/viewupload/684979

Segments, Rays, Distance

http://pdesas.org//EduPortal/Home/viewupload/684980

http://pdesas.org//EduPortal/Home/viewupload/684981

 

Angles

http://pdesas.org//EduPortal/Home/viewupload/684982 

Postulates and Theorems

http://pdesas.org//EduPortal/Home/viewupload/684983

 

Sample Notes - IF I was taking this course, this is what my notes might look like.  Notice the set-up with details on the right page and drawings facing on the left page.

http://pdesas.org//EduPortal/Home/viewupload/684992

DO NOT JUST PRINT THESE NOTES !!! You should write the notes yourself.  I will see this when I check notebooks.

 

 

 

If you are catching up on the notes and the homework, you can use these to keep up to the rest of the class.  If you have questions on any of these, please contact me through the school email system.  fkisner@cmvt.us

 

Chapter 2 - Deductive Reasoning

2.1 If-Then Statements and Converses

http://pdesas.org//EduPortal/Home/viewupload/684985

 2.2 Properties from Algebra

http://pdesas.org//EduPortal/Home/viewupload/684986

2.3 Proving Theorems

http://pdesas.org//EduPortal/Home/viewupload/684987

2.4 Special Pairs of Angles

http://pdesas.org//EduPortal/Home/viewupload/684988

2.5 Perpendicular Lines

http://pdesas.org//EduPortal/Home/viewupload/684989

2.6 Planning a Proof

http://pdesas.org//EduPortal/Home/viewupload/684990

Mr. K's Chapter Notes

http://pdesas.org//EduPortal/Home/viewupload/684991

 

Chapter 3 - Parallel Lines and Planes

 

3.1.  Parallel and Skew Lines

http://pdesas.org//EduPortal/Home/viewupload/684994

3.2  Properites of Parallel Lines

http://pdesas.org//EduPortal/Home/viewupload/685611

3.3  Proving Lines are Parallel

http://pdesas.org//EduPortal/Home/viewupload/684995

3.4  Angles of a Triangle

http://pdesas.org//EduPortal/Home/viewupload/684996

3.5  Angles of a Polygon

http://pdesas.org//EduPortal/Home/viewupload/684997

3.6  Inductive Reasoning

http://pdesas.org//EduPortal/Home/viewupload/684998

Chapter 3 Notes

http://pdesas.org//EduPortal/Home/viewupload/684993

 Parallel Lines Demo

http://pdesas.org//EduPortal/Home/viewupload/689335

 

Chapter 4 Congruent Triangles

Chapter 4 Notes

http://pdesas.org//EduPortal/Home/viewupload/668197

 

4.1 Congruent Figures Ppt.pptx
4.2 Some Ways to Prove Triangles Congruent.pptx
4.3 Using Congruent Triangles.pptx

4.4 Isosceles Triangle Theorem

http://www.pdesas.org/kisnerfc/2015/12/12/640123/file.aspx

4.5 Other Methods of Proving Triangles Congruent

http://www.pdesas.org/kisnerfc/2015/12/12/640124/file.aspx

4.6-4.7 Medians, Altitudes, etc

 

http://www.pdesas.org/kisnerfc/2015/12/18/640560/file.aspx

 

 

CPCTC Worksheet Key:

http://www.pdesas.org/kisnerfc/2015/12/8/639775/file.aspx

 

Chapter 5 Powerpoints

5.1 Properties of a Parallelogram

http://www.pdesas.org/kisnerfc/2016/1/12/641816/file.aspx

5.2 Ways to prove a quadralateral is a parallelogram

http://www.pdesas.org/kisnerfc/2016/1/12/641817/file.aspx

5.3 Theorems about Parallel Lines

 http://www.pdesas.org/kisnerfc/2016/1/12/641818/file.aspx

5.4 Special Parallelograms

 http://www.pdesas.org/kisnerfc/2016/1/12/641819/file.aspx

5.5 Trapezoids

 http://www.pdesas.org/kisnerfc/2016/1/12/641820/file.aspx

 

Chapter 6 Powerpoints

Chapter 6 Notes

http://pdesas.org//EduPortal/Home/viewupload/675251

6.2 Inverses - Contrapositives

http://www.pdesas.org/filehandler.ashx?ID=645265

6.3  Indirect Proof

http://www.pdesas.org/filehandler.ashx?ID=645266

6.3  Answers to Homework Problems

Please do not view this until you have tried the problems.  Thank you.

http://www.pdesas.org/filehandler.ashx?ID=645267

6.4  Inequalities of One Triangle

http://www.pdesas.org/filehandler.ashx?ID=645268

6.5  Inequalities of Two Triangles

http://pdesas.org//EduPortal/Home/viewupload/675216

Review PPT

http://www.pdesas.org/filehandler.ashx?ID=645269

 

 

Chapter 7 - Similar Polygons

7.1 Ratio & Proportion

http://www.pdesas.org/filehandler.ashx?ID=652940

7.2 Properties of Proportion (POP) There are five you should know.

http://www.pdesas.org/filehandler.ashx?ID=652941

7.3 Similar Polygons

http://www.pdesas.org/filehandler.ashx?ID=652942

7.4 AA Similarity Postulate - All you need to prove two triangles are similar is to show that two angles of one are congruent with two angles of the other.

http://www.pdesas.org/filehandler.ashx?ID=652943

7.5 Theorems for Similar Triangles - There are two other ways to prove triangles are similar:  The SAS Similarity Theorem and the SSS Similarity Theorem.  They resemble the same ideas from proving triangles were congruent but instead of the sides having to be congruent (equal), they have to be proportional:  Each set of corresponding sides has exactly the same proportion as the other sets.

http://www.pdesas.org/filehandler.ashx?ID=652944

7.6  Proportional Lengths - Now we can extend what we know from similar triangles first to some other triangles and then to transversals defined by three parallel lines.

This section includes the Triangle Angle Bisector Theorem which is the most unexpected result I have found in all the ideas of basic Geometry.

http://www.pdesas.org/filehandler.ashx?ID=652945

 

 Chapter 8 - Right Triangles

8.1  Similarity in Right Triangles

http://www.pdesas.org/filehandler.ashx?ID=655969

8.2 The Pythagorean Theorem 

http://www.pdesas.org/filehandler.ashx?ID=655970

8.3 The Converse of the Pythagorean Theorem

In addition to using the Pythagorean Theorem to find the missing side of a right triangle, it can be used to prove that a triangle is really a right triangle.  Also, we can use the relationship of the sides to find out if a triangle is really obtuse or acute.

http://www.pdesas.org/filehandler.ashx?ID=655971

 

8.4  Special Right Triangles

There are some right triangles that show up frequently in the world and in math problems.  Two of these are the 45-45-90 triangle and the 30-60-90 triangle.  In this section, we check out easy ways to find missing parts when we know the triangle is one of these.

http://www.pdesas.org/filehandler.ashx?ID=655972

 

Review for Final

This is a document with a copy of the practice problems followed by an answered copy.  The materials you received in paper had spaces where illustrations were missing.  Those problems have been removed from this document.  Also, we did not all get to the last material on the trig ratios and circles.  Those questions will not be on the final.

http://pdesas.org//EduPortal/Home/viewupload/656985