Coordinate Geometry Review & Solutions

You can access the Coordinate Geometry review here!

Solutions are available here!

As an added bonus, you can check the solutions to today's Geogebra adventure here!

Self Checking Fact Finder!

You can check your solutions using the fact answers here!

Wheel of Theodorus Extra Credit Art Project

Create a Wheel of Theodorus neatly and in color.  Mark the unit measures of all of your triangles sides.  Feel free to decorate your wheel in a way that demonstrates this spiral in the real world (it's out there)!  Attach a lined sheet of paper with your calculations for the first 8 triangles.

Instructions

1. Create an isosceles right triangle of a particular unit length of your choosing (too big or too small will make this very difficult, so try to plan ahead).
2. Add another unit length and right angle to the hypotenuse of your original right triangle.
3. Make a right triangle out of the new unit length and previous hypotenuse.
4. Keep adding new unit lengths to the previous hypotenuse at right angles to build new right triangles.
5. When you get to the stage where your right triangles will overlap previous right triangles, draw your hypotenuse toward the center of the spiral but do not mark over previous drawings.
6. Remember to label your figure with all of the dimensions of your successive right triangles.  If a hypotenuse has a length that is a rational number, demonstrate that you recognize this fact.  For example, since sqrt(4)=2, show this on your project.

Grading

• Include a title for your picture
• On the front of your picture, include your signature and the date.
• Label all triangle legs and hypotenuses with appropriate lengths.
• Conjoin each new triangle with the hypotenuse of the previous right triangle.  
• Make sure your project is neat!
• Use color unless you mean to emphasize contrast by using white and black.
• Write your labels using simplified radicals unless they can be simplified to rational numbers.  For example, you might label a hypotenuse sqrt(9)=3.
• Attach a lined sheet of paper to your art containing your calculations to find the lengths of segments using the Pythagorean Theorem for your first 8 triangles.

This guy has a pretty good method!

Be warned!  I have spent a good amount of time looking at these online.  If you copy a project from online, you will not only receive no extra credit, but you will be penalized for your devious plot.  Be original, be creative, be like Frankie - do it your way.  

This project must be submitted by Friday, 1/27/2017, by the end of the day.

Extra Credit: Math Journal

Good afternoon -

I hope everyone is having a great break!  As you know, we are currently working on proving triangles congruent.  One of the issues that continues to come up while writing proofs is the proper identification of reasons for each statement.  To this end, I am offering an extra credit project that I hope will help.

You will be making a compendium of the postulates, theorems, and definitions (abbreviated p/t/d) that we have had so far in the class.  This is quite a project, as there have been many postulates, theorems, and definitions.  It will require some time to complete.  Don't expect to be able to start this on Sunday and finish in time.  Here are the requirements:

• Must be done in a composition notebook.  The most important feature is that pages cannot be added or removed from the composition notebook.
• You must copy down each p/t/d exactly as they are written in the book.  If it has an official 'name', you may title it that, otherwise, title it with the number of the theorem.
• Each p/t/d must be accompanied with an example.  In most cases, this will include a figure that is appropriate to the situation.  A straight edge should be used for all straight lines.  
• If the p/t/d has an abbreviation that can be used in a proof, you may put that in parentheses after the p/t/d.  
• While you are not required to do a single p/t/d per page, no entry should span two pages (don't begin a p/t/d at the bottom of one page and continue it at the top of the next).  This is a reference book, so things should be orderly and easy to find.

You must submit Chapters 1 through 3 to me upon our return to school (1/9/2017).  If, for some reason, you do not feel that you will be able to do that, you need to get in contact with me ASAP.

Below, you can find a list of the p/t/ds that I am expecting to see from Chapters 1 through 3.  Scroll to the bottom for an example of what an entry might look like.

Chapter 1(1.1-1.4):

Postulates

·      1-1-1

·      1-1-2

·      1-1-3

·      1-1-4

·      1-1-5

·      1-2-2: Segment Addition Postulate

·      1-3-2: Angle Addition Postulate

Theorems

·      None for these sections

Definitions

·      Point

·      Line

·      Plane

·      Collinear

·      Coplanar

·      Segment

·      Endpoint

·      Opposite Rays

·      Coordinate

·      Distance

·      Congruent Segments

·      Midpoint

·      Angle

·      Interior of an Angle

·      Exterior of an Angle

·      Acute Angle

·      Right Angle

·      Obtuse Angle

·      Straight Angle

·      Congruent Angles

·      Adjacent Angles

·      Linear Pair

·      Complementary Angles

·      Supplementary Angles

·      Vertical Angles

Chapter 2(2.1-2.3,2.5-2.7):

Postulates

·      None for these sections.

Theorems

·      Thm. 2-6-1: Linear Pair Theorem

·      Thm. 2-6-2: Congruent Supplements Theorem

·      Thm. 2-6-3: Right Angle Congruence Theorem

·      Thm. 2-6-4: Congruent Complements Theorem

·      Thm. 2-7-1: Common Segments Theorem

·      Thm. 2-7-2: Vertical Angles Theorem

·      Thm. 2-7-3

Definitions

·      Inductive Reasoning

·      Conjecture

·      Conditional Statement

o   Hypothesis

o   Conclusion

o   Truth Value

o   Converse

o   Inverse

o   Contrapositive

·      Deductive Reasoning

Laws

·      Law of Detachment

·      Law of Syllogism

 Properties

·      Properties of Equality

o   Addition Property of Equality

o   Subtraction Property of Equality

o   Multiplication Property of Equality

o   Division Property of Equality

o   Reflexive Property of Equality

o   Symmetric Property of Equality

o   Transitive Property of Equality

o   Substitution Property of Equality

·      Properties of Congruence

o   Reflexive Property of Congruence

o   Symmetric Property of Congruence

o   Transitive Property of Congruence

Chapter 3(3.1-3.3):

Postulates

·      3-2-1: Corresponding Angles Postulate

·      3-3-1: Converse of the Corresponding Angles Postulate

·      3-3-2: Parallel Postulate

Theorems

·      Thm: 3-2-2: Alternate Interior Angles Theorem

·      Thm: 3-2-3: Alternate Exterior Angles Theorem

·      Thm: 3-2-4: Same-Side Interior Angles Theorem

·      Thm: 3-2-4: Same-Side Exterior Angles Theorem

·      Thm: 3-3-3: Converse of the Alternate Interior Angles Theorem

·      Thm: 3-3-4: Converse of the Alternate Exterior Angles Theorem

·      Thm: 3-3-5: Converse of the Same-Side Interior Angles Theorem

·      Thm: Converse of the Same-Side Exterior Angles Theorem

·      Thm: 3-4-1

·      Thm: 3-4-2 Perpendicular Transversal Theorem

·      Thm: 3-4-3 Lines perpendicular to a transversal theorem

Definitions

·      Parallel Lines

·      Perpendicular Lines

·      Skew Lines

·      Parallel Planes

·      Transversal

·      Corresponding Angles

·      Alternate Interior Angles

·      Alternate Exterior Angles

·      Same-Side Interior Angles

·      Same-Side Exterior Angles

Here is an example of what an entry in your math journal might look like.

SSS and SAS Postulates

The following document should be copied into your notebook as our notes for the day (section 4.4).  You should do your best to answer the questions that are asked using the provided examples as a guide.

Once you have copied down the notes, you may begin working on this worksheet.

I will be looking for completed notes tomorrow.

Also tomorrow is a homework check on assignments 19-21 and a quiz on sections 4.1-4.3.

Proving Triangles Congruent by Definition

You can access the proof prompts here.

Remember, you need to copy the givens, figure, and what you are trying to prove onto your paper before you complete the proof.  These are part of the proof.

Tomorrow, instead of collecting this work, I will randomly select one of the 4 proofs and ask you to complete it in class.  I am available before school if you have any questions about the proofs.

Review Solutions

Here they are!