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Segment Constructions Module 1 Lesson 2

Segment Constructions Module 1 Lesson 2. Image courtesy of Microsoft. Tools for Constructions. All Images courtesy of Microsoft. Constructing Congruent Segments.

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Segment Constructions Module 1 Lesson 2

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  1. Segment ConstructionsModule 1 Lesson 2 Image courtesy of Microsoft

  2. Tools for Constructions All Images courtesy of Microsoft

  3. Constructing Congruent Segments Let’s say you are an interior designer, a construction foreman, an artist, or just a kid trying to draw up some plans to build a half pipe or a dog house. Whatever the reason, you just need to have two congruent segments to begin your task. What if you do not have a ruler? What if you do but the segment you need is not easily measured by your ruler?

  4. All Images courtesy of Microsoft Constructing Congruent Segments

  5. Constructing Congruent Segments If you are trying to draw a figure, you would want the figure to be as accurate as possible. If you have a line segment in your figure that you need to reproduce, where do you begin? If you do not have a ruler, how can you construct a second segment of equal length?

  6. Constructing Congruent Segments This is actually quite simple if you have a compass. If you do not, you can build a make-shift compass pretty easily with a push pin (or something similar), a piece of string, and a pencil!

  7. Constructing Congruent Segments Near your segment, draw a dot on your paper – consider about how far apart the lines need to be before you do this. That point will be an endpoint of the second line you draw.

  8. Constructing Congruent Segments We’ll label our endpoints and the point we just drew for clarification. Using the compass, place the point of the compass on endpoint A. B A C

  9. Constructing Congruent Segments Now, open your compass so that the pencil (writing end) is on the other endpoint, B. B A C

  10. Constructing Congruent Segments Without changing the compass width, place the point of the compass that was on A on point C. Now draw an arc with the compass near the area that you want the segment to end. B A C

  11. Constructing Congruent Segments The arc gives us a set of points that are equidistant from C. This means we can use any point on the arc. When we connect that point to C, we will have a segment that is congruent to AB. B A C

  12. Constructing Congruent Segments After you have drawn a segment from endpoint C your drawing should look like this. B D A C

  13. Constructing Congruent Segments Congratulations! You have constructed a pair of congruent line segments without a ruler! B D A C

  14. Constructing Perpendicular Bisector to a Segment Now let’s construct a perpendicular bisector to the line AB B A

  15. Constructing Perpendicular Bisector to a Segment Our first step is to make 4 arcs around the line AB. To do this we need to place the point of the compass on an endpoint, let’s start with A. Open the compass so it is just a little more than half the length of AB. B A

  16. Constructing Perpendicular Bisector to a Segment And again, be careful not to change the width of the compass, draw an arc above AB and then draw an arc below AB. B A

  17. Constructing Perpendicular Bisector to a Segment Repeat that process from point B. You will now have two pair of intersecting arcs. B A

  18. Constructing Perpendicular Bisector to a Segment With a ruler, connect the intersection points of the arcs with a line. B A

  19. Constructing Perpendicular Bisector to a Segment Congratulations! You now have a perpendicular bisector of AB! Let’s call this line n. n B A

  20. Constructing Perpendicular Bisector to a Segment But wait! There is more!!! Because we have bisected AB with n, we found the point that bisects the segment, this point is called the midpoint! We can now draw an infinite number of lines through that point! This means we can draw an infinite number of bisectors of AB, with just n being the perpendicular bisector. n A B

  21. Constructions In Lesson 1 you learned about the midpoint of a segment. You also learned that a bisector passes through the midpoint of a segment. It is important that you recognize that not only have you been able to construct a perpendicular bisector, you have found the midpoint of AB. Two birds. One Stone! Nice job  n A B

  22. Constructions • If we label the midpoint, M, we can say a bit more about this figure. • We can easily say: • • • • • n A B M

  23. Constructions What other figures can you construct with your compass? Throughout the course you will learn how to construct other geometric figures. If you understand the basics (copying a segment and constructing a perpendicular bisector) you will be able to do future constructions with ease. If you do not quite understand the process please let your teacher know so that he/she may work with you now. This will make things easier later on! Good luck and happy constructing!

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