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6.3 Applying Properties Relating Parallel Lines and Planes

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6.3 Applying Properties Relating Parallel Lines and Planes

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This image of the chapter 6 review packet shows a proof that involves parallel lines and parallel planes. Some yes or no questions relating to parallelism are also in the image, which provides more information on different situations that could arise in proofs. The proof shown in the picture also demonstrates how a knowledge of the polygons from chapter 5 is necessary in the proofs of chapter 6.

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6.3 Recognizing Lines Parallel To Planes, Parallel Planes, And Skew Lines

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6.3 Recognizing Lines Parallel To Planes, Parallel Planes, And Skew Lines

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This 6.3 note sheet is very useful because it has the definition of skew lines and multiple theorems relating parallel lines and parallel planes, all of which are to be used in proofs. It is a helpful note set because an image is drawn for every theorem. Therefore, if one were to read them, they could easily recreate the image presented by the theorem because diagrams are given. This makes each proof much easier to visualize.

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6.2 Applying The Perpendicularity Of A Line And A Plane Theorem

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6.2 Applying The Perpendicularity Of A Line And A Plane Theorem

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This is an image of one of the examples from my 6.2 notes. As mentioned before, chapter 6 is very cumulative. This proof, although the conclusion to proving AB congruent to CB, includes concepts about planes that are necessary to know. This proof is also an example of one of the theorems relating perpendicularity of lines to planes. By using this theorem, often, two right angles are proven, and are used in congruent triangle proof a lot of the time.

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6.2 Recognizing A Line's Perpendicularity to a Plane

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6.2 Recognizing A Line's Perpendicularity to a Plane

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This 6.2 note sheet is very helpful because it includes the definition of a line perpendicular to a plane, the theorem of proving a line perpendicular to a plane, and two examples with diagrams. The first example shows the conclusions that can be made, given that one lines is perpendicular to a plane. The second example shows that in order for a line to be perpendicular to a plane, it must be perpendicular to TWO distinct lines- not one.

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6.1 Applying Postulates Concerning Lines and Planes

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6.1 Applying Postulates Concerning Lines and Planes

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This image from my geometry book has the two postulates listed concerning lines and planes. These example drawings next to them show the significance in being able to prove a figure is a plane figure, demonstrating how this chapter is very cumulative. These two postulates are important because they help determine whether or not points on certain planes and whether or not certain lines determine planes.

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It is crucial to know these four methods of identifying planes because in every following proof, a plane figure must be proved. The ultimate conclusion cannot be proven until it is established that certain figures are planes. As the image shows below, the four methods of identifying planes are: 3 non-collinear points, a line and a point not on the line, two intersecting lines, and two parallel lines.

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This is an image of the 6.1 notes from class, which discusses the relationship between lines and planes. It is very useful because it includes the basic information on the intersection of planes. Much of the information on this note sheet was used later in proofs and used as basic reasons for the statements in proofs. The notes explain that the one point of intersection when a line intersects a plane is called the foot and that the intersection of two planes is a line.

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This chapter did not go as well as I had hoped. I worked very hard on my homework, though. I made sure that I looked at each problem thoroughly before answering it or leaving it blank. I always came in to get help. I went to the math lab which was extremely useful and I went in early to see Mrs. Kudlov which was also very helpful. I learned during this chapter that using props is almost necessary in visualizing the proofs. It is nearly impossible to picture the 3-dimensional figures on a 2-dimensional piece of paper. That is why actually seeing a problem before my eyes was so important. I also took time in correcting my homework, not just writing the answers but actually trying to understand why my answers were wrong. I continued the good practice of drawing diagrams from last chapter as well. Because I struggled a lot with this chapter, I know that this Padlet is going to be so useful for my when preparing for finals. I may look back on it and not only will I remember the learning targets of this chapter, but I will see SPECIFIC examples from the actual note sheets I took in class. There was not one particular learning target I struggled with- my only struggle was in visualizing the 3-dimensional figures. As for the future, I hope to further develop my skills in analyzing 3-dimensional figures because I believe that once I master that, proofs will become much easier considering I understand the theorems relating to planes.