Chapter 2 Learning Targets by MARGOT OMALLEY

LT #1 - I can recognize the need for clarity and concision in proofs

momalley3 — 2017-09-12 00:02:38 UTC

Proofs need to be clear because now as we have learned so many properties, it is important to know them to distinguish between them. You need to know when one is acceptable to use and when it is not. There are many clues in the problems when which property should be used (bisection/trisection indicates multiplication/division properties and not subtraction/addition properties). Also if the wording is off, it can be misinterpreted and points can be taken off. Here are five problems (#3-7) that include proofs. In #5, I should have used the division property and not the multiplication property to show that the segments are congruent. This homework is helpful because each of these problems requires being precise in order to prove what it is asking.

LT #7 - I can apply the subtraction properties of segments and angles

momalley3 — 2017-09-12 00:02:53 UTC

The subtraction property is: if coungruent angles/segments are subtracted from congruent angles/segments, then their differences are congruent. The reflexive property (where an angle is congruent to itself) can come into play here to help prove how two angles are congruent. This source is useful because it has problems that were beneficial to my learning and helped clear my confusion.

LT #6 - I can apply the addition properties of segments and angles

momalley3 — 2017-09-12 00:03:18 UTC

The addition property theorem is: if congruent angles/segments are added to congruent angles/segments, then their sums are congruent. If you wanted to figure out if an angle was congruent to another one and you had parts connected through the given, you could possibly use this property (as long as it is not multiplication/division/subtraction). This source is useful because it helps you plan out your proof and gives different examples that were beneficial to my learning.

LT #5 - I can prove angle congruent by using complementary and supplementary angle theorems

momalley3 — 2017-09-12 00:03:55 UTC

For problems involving complementary and supplementary angles, there equations that must be used. For finding the complement, 90-x=m< must be used and for the supplement, 180-x=m must be used (x=the angle). In #21 and #22, these are used to find either the complement or supplement along with other things such as 4 times the complement. These problems are a good examples because it makes me apply what I already know and put it into an algebraic equation to figure out what the comp/supp angle is. In proofs it can be useful to use these theorems to prove something is a right or straight angle.

LT #3 - I can recognize complementary and supplementary angles

momalley3 — 2017-09-12 00:04:35 UTC

Complementary angles are two angles that sum to 90 degrees or a right angle. Supplementary angles are two angles that sum to 180 degrees or a straight angle. This video is helpful because it goes over the fundamentals and it is key to have strong fundamentals so you can build off of that and apply it to problems. He gives information on how to distinguish between complementary and supplementary angles and then he shows a diagram and explains why some angles are complementary/supplementary to each other and why others are not.

LT #2 - I understand the concept of perpendicularity

momalley3 — 2017-09-12 00:05:00 UTC

Perpendicularity is when two lines intersect at right angles. In a proof in the reasoning column you would say: if two lines (rays or segments) intersect at right angles, then the lines are perpendicular. This does not work for saying angles are perpendicular to each other because segments/rays/lines must intersect at right angles. Perpendicularity should not be assumed. In this homework, perpendicular segments are mentioned in #10. You can use the given that two perpendicular segments to go to the next statement that the angle is a right angle (because of the definition of perpendicular). This homework is helpful because I know when to apply perpendicularity and when I can't.

LT #8 - I can apply the multiplication and division properties of segments and angles

momalley3 — 2017-09-17 15:28:51 UTC

The multiplication property is: if angles are congruent, then their like doubles/triples are congruent. The division property is: if angles are congruent, then their like halves/thirds are congruent. The multiplication property starts small and ends big; division property is the opposite. This is used with bisectors and trisectors. This source helped me because the examples cleared confusion and it went over the fundamentals which are essential to understanding how to do more complex problems.

LT #9 - I can apply the transitive properties of angles and segments

momalley3 — 2017-09-17 15:29:15 UTC

The transitive property is a special case of the substitution property. It can be used to show congruence of angles or segments. For a proof in the reasoning column you can use this: If two angles are congruent to the same (or congruent) angles (or segments), then they're congruent to each other. In problem five, I used that in my final reasoning to explain how angles two and three are congruent to each other.

LT #10 - I can apply the Substitution Property

momalley3 — 2017-09-17 15:29:42 UTC

The substitution property includes the transitive property, which is a special case. For a proof, this is the statement you can use in the reasoning column (it is okay to put "substitution"): If two angles are congruent, then they are complementary to the same angle. This property can be used in algebra and in geometry, but in geometry it is used when variables are not present and when sums/equations are referenced (not explicitly too). It can be used when you are trying to prove an angle is supplementary/complementary to another angle and both of those angles are congruent to the same angle. This source is useful because it shows examples and explains them. It also distinguishes between the transitive and substitution properties and when to use them.

LT #11 - I can recognize opposite rays

momalley3 — 2017-09-17 16:26:17 UTC

Opposite rays are two collinear rays that share a common endpoint and extend in different directions. They must follow all of those characteristics or else they cannot be opposite rays. This section from our notes does a nice job explaining opposite rays and lists different characteristics as to why the examples are not opposite rays. I can use this information and apply it in proofs when looking at diagrams (because it can't be used as a step in proofs).

Chapter Reflection

momalley3 — 2017-09-17 19:56:42 UTC

I included these learning targets because for studying for this test and the final, I have specific examples and resources I can use. On the quiz for this chapter, I did not do so well, but that was because I did not separate each of the properties and definitions from each other and so I have improved through these writing these learning targets and writing down all of them on a sheet to keep track of them. From writing down the definitions, it became easier to apply them in proofs and with the help of these sources, I have a greater understanding. I am now more confident in my abilities to apply them and for some of them such as complementary and supplementary angles (I was able to understand this right away), I still have a great understanding of this.