* means degrees
In this unit I was suppose to learn:
-Patterns and Inductive Reasoning
-Points, Lines, and Planes
-Segments and Their Measures
-Angles and Their Measure
-Segment and Angle Bisectors
-Angle Pair Relationships
-Perimeter, Circumference, and Area
-Conditional Statements
-Biconditional Statements
-Deductive Reasoning
-Reasoning with Properties from Algebra
-Points, Lines, and Planes
-Segments and Their Measures
-Angles and Their Measure
-Segment and Angle Bisectors
-Angle Pair Relationships
-Perimeter, Circumference, and Area
-Conditional Statements
-Biconditional Statements
-Deductive Reasoning
-Reasoning with Properties from Algebra
Four Concepts I mastered are:
-Angles and Their Measure
An angle is two different rays with the same start point and go in different directions. The rays are the sides of the angle and the start point is the vertex of the angle. An angle can have up to 3 names, if you have an angle with sides GH--> and GI-->, you could name it <HGI, <IGH, or <G. G is the vertex of the angle and you can only name an angle by the vertex if it is by itself and there are no angles connected to it. You measure an angle with a protractor and use units called degrees. For example: <HGI has a measure of 120* and you can write that as m<HGI=120*. You also have an angle addition postulate that says if you have two adjacent angles and you add them together you get the whole angle. For example: m<EFD+ m<DFG= m<EFG. You can classify angles, too. They can be classified as acute, right, obtuse, and straight. Acute is if the angle is less that 90*, Right is if the angle is 90*, Obtuse is if the angle is more than 90*, and Straight is if it is 180*.
-Conditional Statments
A conditional statement is a statement that has two parts, a hypothesis and a conclusion. It can be written in the if-then form. The if part is the hypothesis and the then part is the conclusion. For example: If there's a rainbow, then it rained. There's a rainbow is the hypothesis and it rained is the conclusion. You can also write different versions of the conditional statement such as, the converse, inverse, and contrapostive. The coverse is formed by swiching the hypothesis and conclusion. For example: If it rained, then there a rainbow. The inverse is formed by negating the hypothesis and conclusion. For example: If there's not a rainbow, then it didn't rain. The contrapositive is formed by doing the inverse of the converse. For example: If it didn't rain, then there isn't a rainbow.
-Biconditional Statements
A biconditional statement is a statement with a hypothesis and conclusion in the if-and only-if form. For example: I am hungry, only if my stomach is empty.
-Deductive Reasoning
Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a logical statement. For example: Bob only likes red apples, so if I gave him a green apple he wouldn't like it. Sometimes conditional and biconditional statements can be written in symbolic notation. They are:
Hypothesis- p
Conclusion- q
Conditional Statement- p-->q
Converse- q-->p
Inverse- ~p-->~q
Contrapostive- ~q-->~p
Biconditional- p<-->q
Deductive Reasoning also has 2 laws to go by the Law of Detachment and the Law of Syllogism. The Law of Detachment says if p-->q is a true conditional statement and p is true, then q is true. For example: If the train is moving, then it's on train tracks. The hypothesis, the train is moving, is true, so therefore the conclusion, it's on train tracks, is true. The Law of Syllogism says if p-->q and q-->r are true conditional statements, then p-->r is true. For example: If you are asleep, then your eyes are closed. If your eyes are closed, then you can't see what's happening around you. So, if you are asleep, then you can't see what's happening around you.
An angle is two different rays with the same start point and go in different directions. The rays are the sides of the angle and the start point is the vertex of the angle. An angle can have up to 3 names, if you have an angle with sides GH--> and GI-->, you could name it <HGI, <IGH, or <G. G is the vertex of the angle and you can only name an angle by the vertex if it is by itself and there are no angles connected to it. You measure an angle with a protractor and use units called degrees. For example: <HGI has a measure of 120* and you can write that as m<HGI=120*. You also have an angle addition postulate that says if you have two adjacent angles and you add them together you get the whole angle. For example: m<EFD+ m<DFG= m<EFG. You can classify angles, too. They can be classified as acute, right, obtuse, and straight. Acute is if the angle is less that 90*, Right is if the angle is 90*, Obtuse is if the angle is more than 90*, and Straight is if it is 180*.
-Conditional Statments
A conditional statement is a statement that has two parts, a hypothesis and a conclusion. It can be written in the if-then form. The if part is the hypothesis and the then part is the conclusion. For example: If there's a rainbow, then it rained. There's a rainbow is the hypothesis and it rained is the conclusion. You can also write different versions of the conditional statement such as, the converse, inverse, and contrapostive. The coverse is formed by swiching the hypothesis and conclusion. For example: If it rained, then there a rainbow. The inverse is formed by negating the hypothesis and conclusion. For example: If there's not a rainbow, then it didn't rain. The contrapositive is formed by doing the inverse of the converse. For example: If it didn't rain, then there isn't a rainbow.
-Biconditional Statements
A biconditional statement is a statement with a hypothesis and conclusion in the if-and only-if form. For example: I am hungry, only if my stomach is empty.
-Deductive Reasoning
Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a logical statement. For example: Bob only likes red apples, so if I gave him a green apple he wouldn't like it. Sometimes conditional and biconditional statements can be written in symbolic notation. They are:
Hypothesis- p
Conclusion- q
Conditional Statement- p-->q
Converse- q-->p
Inverse- ~p-->~q
Contrapostive- ~q-->~p
Biconditional- p<-->q
Deductive Reasoning also has 2 laws to go by the Law of Detachment and the Law of Syllogism. The Law of Detachment says if p-->q is a true conditional statement and p is true, then q is true. For example: If the train is moving, then it's on train tracks. The hypothesis, the train is moving, is true, so therefore the conclusion, it's on train tracks, is true. The Law of Syllogism says if p-->q and q-->r are true conditional statements, then p-->r is true. For example: If you are asleep, then your eyes are closed. If your eyes are closed, then you can't see what's happening around you. So, if you are asleep, then you can't see what's happening around you.
Chapter 1.1 Patterns and Inductive Reasoning
I know I have mastered this concept because I learned how to figure out a pattern of numbers in like 2nd grade. An example of applying this to real life is:
You have a test that says to explain the pattern and find the next 3 numbers of 1, 3, 5, 7, 9.
You could say the numbers are consecutive odd numbers or that you add 2. The next three numbers are 11, 13, 15.
I don't have any difficulty understanding anything in this section. On the next test on this I expect to get 100% and I plan to do this by figuring out the pattern.
You have a test that says to explain the pattern and find the next 3 numbers of 1, 3, 5, 7, 9.
You could say the numbers are consecutive odd numbers or that you add 2. The next three numbers are 11, 13, 15.
I don't have any difficulty understanding anything in this section. On the next test on this I expect to get 100% and I plan to do this by figuring out the pattern.
Chapter 1.2 Lines, Points, and Planes
I know I have mastered this concept because it's easy to understand. An example
of applying it to real life is:
I can create my own ruler using the ruler
postulate which says every point on a line can be paired with a real number.
Then, I can measure with my own units.
I don't have difficulty understanding this concept at all. On the next test I hope to get 100% and I am going to get this by reviewing the section.
of applying it to real life is:
I can create my own ruler using the ruler
postulate which says every point on a line can be paired with a real number.
Then, I can measure with my own units.
I don't have difficulty understanding this concept at all. On the next test I hope to get 100% and I am going to get this by reviewing the section.
Chapter 1.3 Segments and Their Measures
I know I have mastered this concept because I can apply it to real life. For example:
A gas station is inbetween my house and school. From my house to the gas
station it is 2 miles and from my house to school it is 5 miles. How many miles
is it from the gas station to school?
I can figure this out by
using the segment addition postulate which is AB+BC=AC. So, 2+GS=5. GS=3 so
from the gas station to school is 3 miles.
I don't have
difficulty undestaning anything because everything is pretty much
straight-forward. On the next test I want to get 100% on this part and I am
going to do this by reading the question carefully.
A gas station is inbetween my house and school. From my house to the gas
station it is 2 miles and from my house to school it is 5 miles. How many miles
is it from the gas station to school?
I can figure this out by
using the segment addition postulate which is AB+BC=AC. So, 2+GS=5. GS=3 so
from the gas station to school is 3 miles.
I don't have
difficulty undestaning anything because everything is pretty much
straight-forward. On the next test I want to get 100% on this part and I am
going to do this by reading the question carefully.
Chapter 1.4 Angles and Their Measures
I know I have mastered because I understand what an angle is and how to measure and name it. I can apply this to real life by:
What kind of angle is in this picture of a baseball diamond?
It is a right angle and I know because only right angles measure 90*.
I don't have any difficulty understanding this concept because I think angles are one of the most easy things to understand. On the next test I believe I will get 100% and I will achieve this by figuring out the angles measures.
What kind of angle is in this picture of a baseball diamond?
It is a right angle and I know because only right angles measure 90*.
I don't have any difficulty understanding this concept because I think angles are one of the most easy things to understand. On the next test I believe I will get 100% and I will achieve this by figuring out the angles measures.
Chapter 1.5 Segment and Angle Bisectors
I know I have mastered this concept because it is simple and understandable. I can apply it to real life by:
If you wanted to cut a baseball field in half you could use the angle bisector. If a baseball field is 90*, then when you use the bisector is would be cut in half so each half would be 45*.
I definitely don't any problems with this concept because this is the easiest one, all you really do is cut the angle or segment in half. On the next test I better get 100% and I am going to accomplish this by using my math skills and my calculator.
If you wanted to cut a baseball field in half you could use the angle bisector. If a baseball field is 90*, then when you use the bisector is would be cut in half so each half would be 45*.
I definitely don't any problems with this concept because this is the easiest one, all you really do is cut the angle or segment in half. On the next test I better get 100% and I am going to accomplish this by using my math skills and my calculator.
Chapter 1.6 Angle Pair Relationships
I know that I have mastered this concept because I understand what the book and the teacher are talking bout when the say vertical and linear angle. I can apply this to real life by:
If your taking a test and you have a problem that says find the measure of <A, <B, and <C you can figure this out quite simply.
Since <B and the angle with 120* are vertical angles they have the same degrees, so <B=120*. Since <A and <B are linear angles together they equal 180*, so 180-120=60 <A=60*. <A and <C are vertical angles, so <C=60* also.
I don't have any problems with this concept because if you remember which is which you shouldn't have a problem. On the next test I hope to get 100% on this part. I will accomplish this by remembering which is which between the vertical and linear angles.
If your taking a test and you have a problem that says find the measure of <A, <B, and <C you can figure this out quite simply.
Since <B and the angle with 120* are vertical angles they have the same degrees, so <B=120*. Since <A and <B are linear angles together they equal 180*, so 180-120=60 <A=60*. <A and <C are vertical angles, so <C=60* also.
I don't have any problems with this concept because if you remember which is which you shouldn't have a problem. On the next test I hope to get 100% on this part. I will accomplish this by remembering which is which between the vertical and linear angles.
Chapter 1.7 Perimeter, Circumference, Area
I know I have mastered this concept because when the teacher quizzed everyone at
the door I got mine correct. I can apply this to real life by:
Cassandra's block is 100m long and 67m wide. Find the perimeter and area.
p=2l+2w p=2(100)+2(67)= 200+134 p=334
a=lw a=100(67) a=6,700
I don't have any difficulty with this concept because you just have to remember the formulas. On the next test I strive to get 100% and I will do this by memorizing the formulas and using my brain on hard questions.
the door I got mine correct. I can apply this to real life by:
Cassandra's block is 100m long and 67m wide. Find the perimeter and area.
p=2l+2w p=2(100)+2(67)= 200+134 p=334
a=lw a=100(67) a=6,700
I don't have any difficulty with this concept because you just have to remember the formulas. On the next test I strive to get 100% and I will do this by memorizing the formulas and using my brain on hard questions.
Chapter 2.1 Conditional Statements
I know I have mastered this concept because I got 100% on my papers. I can apply this concept to real life because you use conditional statements in real life all the time. For example:
If it's snowing, then it's less than 32*.
I have no trouble at all understanding this concept because it's something we already use without knowing it. On the next test I woulld like to get 100% and I will do this by reading the instructions carefully.
If it's snowing, then it's less than 32*.
I have no trouble at all understanding this concept because it's something we already use without knowing it. On the next test I woulld like to get 100% and I will do this by reading the instructions carefully.
Chapter 2.2 Definitions and Biconditional Statements
I know I have mastered this concept because it's very simular to conditional statments and I have mastered that. I can apply this to real life because just like conditional statements you use it in real life already. For example:
A light is on if and only if there is power going to it.
I have no trouble understanding this concept because just like conditional statements you use it in real life. On the next test I hope to get 100% and I will achieve this goal by memorizing everything and remembering what I already use in real life.
A light is on if and only if there is power going to it.
I have no trouble understanding this concept because just like conditional statements you use it in real life. On the next test I hope to get 100% and I will achieve this goal by memorizing everything and remembering what I already use in real life.
Chapter 2.3 Deductive Reasoning
I know I have mastered this concept because it relates to conditional statements and biconditional statements. I can apply this to real life by:
If you are asleep, then your eyes are closed. If your eyes are closed, then you can't see what's happening around you. So, If you're asleep, then you can't see what's happening around you. The law that says this is possible is the Law of Syllogism and this applies to real life because it helps you draw conclusions.
I have no difficulty with this concept because it's easy after you understand it. On the next test I hope to get 100% on it and I will do this by very carefully reading the directions.
If you are asleep, then your eyes are closed. If your eyes are closed, then you can't see what's happening around you. So, If you're asleep, then you can't see what's happening around you. The law that says this is possible is the Law of Syllogism and this applies to real life because it helps you draw conclusions.
I have no difficulty with this concept because it's easy after you understand it. On the next test I hope to get 100% on it and I will do this by very carefully reading the directions.
Chapter 2.4 Reasoning with Properties from Algebra
I know I have mastered this concept because I have taken Algebra already. I can apply this to real life by:
On the test it asks you to tell what property says If a=b, then a+c=b+c.
You would know it is the addition property because it has addition signs.
I have a little bit of trouble with this one because the questions they ask are very confusing. I hope to better understand this concept by asking questions and rereading. On the next test I hope to get at least a 90% on this part and I hope to achieve this by studying.
On the test it asks you to tell what property says If a=b, then a+c=b+c.
You would know it is the addition property because it has addition signs.
I have a little bit of trouble with this one because the questions they ask are very confusing. I hope to better understand this concept by asking questions and rereading. On the next test I hope to get at least a 90% on this part and I hope to achieve this by studying.