Constructions - Edgenuity (All done!) 100% on assignment PDF

Preview

Summary

I got 100% on this assignment, please be sure to switch up the words so you don't get points taken off. JJJJJJJJJJJJJJJJJJJJJJJJJNFKSBVIKHVDSF...

Description

9/23/2021

Jeweleah Johnson

Geometric Constructions Euclid, a Greek mathematician known as the “Father of Geometry,” wrote the book Elements, which recorded all of the mathematical knowledge of the time in an organized and logical fashion. Since 1482, more than a thousand editions of Elements have been published in many languages. In fact, it was considered to be required reading by all educated people until the twentieth century, and was still being used as a high school textbook as recently as 1980. In Elements, Euclid used construction techniques extensively, and so they have become a part of the geometry field of study. A compass and straightedge are used to create constructions.

As you complete the assignment, keep this question in mind: How can congruent segments and lengths be created with a tool with no marked measurements? In this task, you will apply what you have learned in this lesson to answer this question.

Directions Answer each of the following questions, reading the directions carefully as you go. Refer to the constructions you completed in the previous assignment to help answer the questions.Type all your responses into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the completeness and accuracy of your explanations. Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy. Now, let’s get started!

Copyright © Edgenuity Inc.

Student Guide (continued)

Copyright © Edgenuity Inc.

Student Guide (continued)

Step 1: Copy a segment and an angle. a) Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?

To begin, draw a line that is longer than the segment but not wider than the page's width. This line should be at least 1/2 inch away from the left-hand side. After that, measure the length of the original segment with a compass. Following that step, measure the distance along the compass line. (One end is on the left edge, while the other (the pencil end) is used to mark the section so that it is the same length as the compass)

Either step two or three is the most important step in the process of copying a line segment to ensure that the new line segment is the same length as the original.

b) Explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long as 𝐴𝐵.

Firstly, place the center of your compass on point and adjust the compass width to AB's length. Then place the compass's center on B and draw an arc without altering the compass's width. After that, draw a line from Point A to the arc with your straightedge, this new line segment should now be twice as long as the previous one.

Copyright © Edgenuity Inc.

Student Guide (continued)

c) The construction of copying ∠𝑄𝑃𝑅 is started below. The next step is to set the width of the compass to the length of 𝐴𝐵 . How does this step ensure that the new angle will be congruent to the original angle?

Point S is drawn to resemble point P. PA is measured and copied to point S, resulting in PA = ST. PB's length is measured and transferred to point U, resulting in PB = SU. Concluding that AB = SU. Since all of the sides are congruent, we can conclude that ∠P ≡ ∠S.

d) How is copying a line segment similar to copying an angle?

Copyright © Edgenuity Inc.

Student Guide (continued)

In terms of construction, replicating a line segment and an angle necessitates the use of a set compass width. Thus, copying a line segment is similar to copying an angle because they both utilize the same compass width as the basic tool to replicate a line segment or an angle in both cases.

Step 2: Construct a perpendicular line. a) In the step shown of the construction of a line through a point that is perpendicular to the given line, why must the compass point be placed on points A and B? How would the construction be different if the compass point were placed at random points on the original line?

Because you need to build arcs to make the perpendicular line via the supplied line, the compass point must be set on points A and B. If the compass point was placed at random spots on the original line, the line would not be lined up correctly in the middle and would not be correct.

Copyright © Edgenuity Inc.

Student Guide (continued)

Step 3: Construct an angle and a perpendicular bisector. a) The construction of creating the perpendicular bisector of 𝑃𝑄 is started below. How would the construction be different if you changed the compass setting in the next step of the perpendicular bisector construction?

It will not create a perpendicular bisector. If the compass is the same setting as the first arc and drawn from point B, the points of intersection of the arcs will pass through the midpoint of AB and create a perpendicular bisector. However, if you change the setting of the compass and draw an arc from point B, the points of intersection of the arcs will still create a perpendicular line but will not pass through the midpoint of AB. This would result in the creation of a perpendicular line, but not a perpendicular bisector.

Copyright © Edgenuity Inc....