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.
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.
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