Geometric Constructions

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1 Geometry Name: Part 1: What are Geometric Constructions? Geometric Constructions Go to Answer the following questions. 1. What is a construction? 2. What tools are used in geometric constructions? 3. What tools are you NOT allowed to use in geometric constructions? 4. What is a compass? 5. What is a straightedge? 6. Who was Euclid? What was the title of his book? 7. Why could the Greeks not do arithmetic easily? Part 2: Duplicating Segments, Angles and Triangles Watch the first 30 seconds of the video at (until you see the title Copying the Segment ) 8. Using a straightedge and a pencil, construct the following LK NM Acute PQR 1

2 Copying a Line Segment Watch the video at from :30 to 1:20 (until you see the title Copying the Angle ). You may rewind and re-watch the video. Watch Watch 9. Write the steps to copy a segment in your own words 10. Copy ST at point S. Copy an Angle Watch the video at from 1:20 to 2:10 (until you see the title Make Parallel Lines ). You may rewind and re-watch the video. Watch Watch Write the steps to copy an angle in your own words. 2

3 12. Copy UVW at point V. Copy a Triangle 13. Use your skills from above to copy the triangle XYZ starting at point X. You may re-watch the above videos and/or watch the video at Write the steps to copy a triangle in your own words. 3

4 Part 3: Constructing Perpendicular Lines and Perpendicular Bisectors 14. Go to Define and sketch an example of each of the following. a. Perpendicular: b. Perpendicular Bisector: c. Rectangle: Construct a Perpendicular Line through a Point on the Line Watch the videos on constructing a perpendicular line through a point on the line at and Write the steps to construct a perpendicular line through a point in your own words. 16. Using a compass and straightedge construct a perpendicular line passing through point A. 4

5 Construct a Point on a Line Though a Point Not on the Line Watch the video on constructing a perpendicular line through an external point at and Write the steps to construct a perpendicular line through a point not on the line in your own words. 18. Using a compass and straightedge construct a perpendicular line passing through point B. 5

6 Construct a Perpendicular Bisector Watch the video on constructing a perpendicular bisector of a segment at and A perpendicular bisector forms a 90 o angle with the given line and also finds the. 20. Write the steps to construct a perpendicular bisector in your own words 21. Using a compass and straightedge, to construct a perpendicular bisector of GH. 6

7 Construct a Rectangle 22. Follow the steps to construct a rectangle using a compass and protractor. 1. Construct a perpendicular line at point J. 2. Draw a point on the newly constructed perpendicular line. Name the point L. 3. Construct a perpendicular line at point K. 4. Copy segment JL onto the newly constructed perpendicular line at K. Name this segment KM. 5. Use the straightedge to draw segment LM. Part 4: Construct Angle Bisectors and Parallel Lines 23. Go to Define and sketch an example of each of the following. a. Angle bisector: b. Parallel line: 7

8 Construct an Angle Bisector Watch the videos to construct an angle bisector at and Write the steps to construct an angle bisector in your own words. 25. Using a compass and straightedge to construct the angle bisector of SRT. Name the angle bisector RU. 8

9 Construct a Parallel Lines through a Given Point Watch the videos to construct a parallel lines at and (this video does not start with the given point and line, but uses the same process) 26. Complete the following: If corresponding angles are, then the lines are. 27. Write the steps to construct a parallel line through a given point in your own words. 28. Using a compass and protractor, construct a parallel line through point N and parallel to MP. Name the line NO. 9

10 29. Go to Scroll halfway down the page to Constructions on this site. Choose one of the constructions that you have not already completed. Watch the video. a) What was the name of the construction? b) Write the steps to the construction c) Complete the construction below. 10

11 Geometry HW 12 Name: Geometric Constructions Homework Part 1 and 2 1. Copy the following segments using a compass and straightedge. Name them with a after each letter. For example: original is AB and copy would be A B. a) b) 2. Copy the following segments using a compass and straightedge. a) b) 3. Copy the triangle using a compass and straightedge. 11

12 4. Simplify by distributing and combining like terms a) 4 x + 3 5x b) 3y(y 6) c) 6 3(w + 4) d) 7n 4 n + 4n! e) 3 m + 2 6(m 3) f) 4 2z z + z! 5. FOIL or Distribute and Combine Like Terms a) (x + 3)(x 4) b) (x 5)(x 2) c) (2x + 1)(x 7) d) (x + 9)(3x + 2) 12

13 Geometry HW 13 Name: Geometric Constructions Homework Part 3 1. Construct a perpendicular line for each of the following. a) Construct AB CD. Construct a perpendicular line through point C. Name the line segment CD. b) Construct ST UV. Construct a perpendicular line through point U. Name the line UV. 2. Construct the perpendicular bisector of EF 13

14 3. Construct square SQUA. Steps a. Construct a perpendicular line at point S b. Duplicate SQ onto the new perpendicular line. Name the new segment SA. c. Construct a perpendicular line at point Q. d. Duplicate SQ onto the new perpendicular line at point Q. Name the new segment QU. e. Construct segment UA. 4. Distribute and combine like terms a) 4x(3 + 5x) b) 2(9 7x) c) 5x(x! + 2x 3) d) 6x(2x 1) 5. Factor the following a) 12x + 20x! b) 18 14x c) 5x! + 10x! 15x d) 12x! 6x 14

15 Geometry HW 14 Name: 1. Construct the angle bisector for ABC Geometric Constructions Homework Part 4 2. Construct the angle bisector for DEF 3. Construct a line parallel to AB passing through point C. 15

16 4. Construct a line parallel to EF passing through point G. 5. Duplicate the following by constructing perpendicular segments and duplicating the angles and segements. 6. Factor the following a) 7x + 14 b) 5x! 8x e) 9a! b + 9ab c) 13x! 26x f) 8x! + 16y! d) 4ab 7a 16

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