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Perpendicular Line Constructions Lindsay Chenoweth Jonathan Bojarski

Perpendicular Line Constructions Lindsay Chenoweth Jonathan Bojarski. Introduction. What is a construction? A “drawing” using only a compass and straightedge that renders “exact” results. Construction is not simply drawing, it is like building a drawing.

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Perpendicular Line Constructions Lindsay Chenoweth Jonathan Bojarski

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  1. Perpendicular Line ConstructionsLindsay ChenowethJonathan Bojarski

  2. Introduction • What is a construction? • A “drawing” using only a compass and straightedge that renders “exact” results. • Construction is not simply drawing, it is like building a drawing. • No instrument or surface can actually create exact results. • Why do we need constructions?

  3. Perpendicular Lines • Perpendicular lines: two lines that intersect, and at their intersection form four angles that equal 90 degrees each.

  4. Perpendicular Lines • 3 Constructions of Perpendicular Lines: • Given two points A and B on a line, construct any line perpendicular to the given line. • Given a line and a point A on that line, construct a perpendicular line through point A. • Given a line and a point A off of that line, construct a line from point A perpendicular to the given line.

  5. Construction 1 • Given two points on a line, construct any line perpendicular to the given line. B A

  6. Construction 1 • Step 1: Draw a circle centered at point A.

  7. Construction 1 • Step 2: Draw a circle with the same radius centered at point B.

  8. Construction 1 • Step 3: Draw points at the places where the two circles intersect.

  9. Construction 1 • Step 4: Draw a line that connects the two points. This line should be perpendicular to line AB.

  10. Construction 2 • Given a line and a point A on that line, construct a line perpendicular to that line through A.

  11. Construction 2 • Step 1: Draw a circle of any radius centered at point A.

  12. Construction 2 • Step 2: Draw points at both places where the circle intersects the given line. Name these points B and C.

  13. Construction 2 • Step 3: Draw a circle centered at point B with a radius larger than segment BA. Draw a circle centered at point C with the same radius as circle B.

  14. Construction 2 • Step 4: Draw points at both places where circles B and C intersect. Connect these points with a line. This line should be perpendicular to line BAC through point A.

  15. Construction 3 • Given a line and a point A off of that line, construct a line perpendicular to the given line that runs through point A.

  16. Construction 3 • Step 1: Draw a circle centered at point A that intersects the given line in two places. Draw points where the circle intersects the line. Name these points B and C.

  17. Construction 3 • Step 2: Draw a circle centered at point B with a radius greater than or equal to BA. Draw a circle centered at point C with a radius of CA.

  18. Construction 3 • Step 3: Draw points where these circles intersect. Draw a line that connects this point with point A. This line should be perpendicular to line BC.

  19. Constructions Online http://www.mathsnet.net/campus/construction/i_index.html A3: construction 1 B2: construction 2 B4: construction 3

  20. Question • Using what you know about the different ways to construct perpendicular lines, can you come up with a way to construct parallel lines?

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