Chapter 2.5 Proving Statements About Segments
Let's say you have a problem in math that says this, and the given is KJ=~JM, JM=~ML. Now you have to solve for the variable using the given imformation.
The first one is always given so that's easy. For the second one, I used the transitive property of segment congruence, which is is AB=~CD, and CD=~EF, then AB=~EF, so KJ=~ML. For the third one, I used the definition of congruent segments which is self explanatory. For the fourth one, I substituted the numbers in, so I can start to solve the prolem. For the fifth step, I subtracted 2 from each side and got 3=3x. Finally, for the sixth one, I divided 3 on both sides and came up with x=1.
The first one is always given so that's easy. For the second one, I used the transitive property of segment congruence, which is is AB=~CD, and CD=~EF, then AB=~EF, so KJ=~ML. For the third one, I used the definition of congruent segments which is self explanatory. For the fourth one, I substituted the numbers in, so I can start to solve the prolem. For the fifth step, I subtracted 2 from each side and got 3=3x. Finally, for the sixth one, I divided 3 on both sides and came up with x=1.
Chapter 2.6 Proving Statements About Angles
Now you have a problem that show a picture like this and you are told to complete the statements knowing that <1 and <2 are complementary.
1)If m<3=90*, then m<6=90*. I got this because <3 and <6 are vertical angles.
2)If m<1=47*, then m<2=43*. Since <1 and <2 are complementery the add up to 90*.
1)If m<3=90*, then m<6=90*. I got this because <3 and <6 are vertical angles.
2)If m<1=47*, then m<2=43*. Since <1 and <2 are complementery the add up to 90*.
Chapter 3.1 Lines and Angles
If you were to relate this to real life these lines could be roads that intersect and form angles. Now, a math problem might ask you to name the angles formed by the transversal. For example:
1)<1 and <5 are corresponding angles. This is true because <1 and <5 are in corresonding positions.
2)<3 and <6 are alternate interior angles. Since <3 and <6 are on opposite sides of the transversal and one is on the top and the other on the bottom between the two lines.
3)<4 and <6 are consecutive interior angles. This is correct because <4 and <6 are on the same side of the transversal and they are inbetween the two lines.
1)<1 and <5 are corresponding angles. This is true because <1 and <5 are in corresonding positions.
2)<3 and <6 are alternate interior angles. Since <3 and <6 are on opposite sides of the transversal and one is on the top and the other on the bottom between the two lines.
3)<4 and <6 are consecutive interior angles. This is correct because <4 and <6 are on the same side of the transversal and they are inbetween the two lines.
Chapter 3.2 Proof and Perpendicular Lines
This chapter is mostly about perpendicular lines, so let's pretend those 2 intersecting lines are 2 intersecting roads and you are turning left forming <1 and you want to figure out what degrees the angle you made was. Theorem 3.3 says if two lines are perpendicular , then they inersect to form four right angles. So, by saying that, all of those angles are 90* because perpendicular lines are all 90* including the one you made.
Chapter 3.3 Parallel Lines and Transversals
On a test you may have a problem like this and the directions say to figure out the angle measures of <1 and <2. You can figure out the m<2 because it is vertical angles with the other angle, so m<2=60*. You can figure out the m<1 because it is alternate interior angles with <2, so m<1=60* too.
Chapter 3.4 Proving Lines are Parallel
This chapter is all about proving lines are parallel by using the converse of different postulates and theorems. So, you will find a question asking if you can prove that the lines a parallel. For this example I have here you can prove it because of the Corresponding Angles Converse Postulate which states that if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Chapter 3.5 Using Properties of Parallel Lines
To apply this to real life you could say that all of the vertical lines are the vertical pieces of a fence and the diagonal piece is the one that holds them all together. When you put the fence up you noticed that mlln and nllo. So you know they are all parallel because of Theorem 3.11 which states if two lines are parallel to the same line, then they are parallel to each other. Also, using the transitive property of equality you know mllo.
My Goals
The goals I had for the last card marking were pretty much met because I got 100% on my last test on chapter 3. My goal for this card marking is to get 100% again and keep up the good work, espeially since I don't want to take the midterms.