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Classic Constructions

Classic Constructions. Ryan Caliguri – WMHS Jeffrey Wainz - WMHS. G.SR.07.02. G- Geometry SR- Spatial Reasoning and geometric modeling 07- 7 th grade curriculum 02- The second type of concept in that section. G.SR.07.02. Terminology Informal justifications. G.SR.07.02.

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Classic Constructions

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  1. Classic Constructions Ryan Caliguri – WMHS Jeffrey Wainz - WMHS

  2. G.SR.07.02 G- Geometry SR- Spatial Reasoning and geometric modeling 07- 7th grade curriculum 02- The second type of concept in that section

  3. G.SR.07.02 Terminology Informal justifications

  4. G.SR.07.02 • Basic Geometric Constructions • Perpendicular Bisector • Equilateral Triangle • Angle Bisector • Inscribed Circle • Circumscribed Circle

  5. Terminology Compass: an adjustable device used to construct circles Straight Edge: any tool that is used to draw straight lines during constructions

  6. Terminology Bisector: line that divides a segment or angle into two equal halves Perpendicular: lines that intersect at 90 degree angles

  7. Terminology Equilateral Triangle: triangle with 3 congruent sides and angles Circumscribed Circle: a circle drawn around a triangle

  8. Terminology Vertex: the point where two lines intersect to form an angle Inscribed Circle: a circle drawn inside of a triangle

  9. Terminology Line: a figure that goes on forever in 2 directions Line Segment: a line with a defined length

  10. Terminology Ray: a figure that goes on forever in one direction and ends in a point on the other Radius: a line that goes from the center of the circle to the outside

  11. Perpendicular Bisectors Cuts a line in half New line is perpendicular to the original segment

  12. Constructing a Perpendicular Bisector

  13. Angle Bisectors Cuts an angle in half Two new created angles are congruent

  14. Constructing Angle Bisectors

  15. Equilateral Triangle A triangle with sides of exactly the same side All angles are 60 degrees

  16. Constructing Equilateral Triangles

  17. Inscribed Circle Creates a circle using angle bisectors The circle touches all three sides of the triangle

  18. Inscribed Circle Prerequisites Angle bisectors Perpendicular lines through a point

  19. Inscribed Circle

  20. Circumscribed Circle Creates a circle using perpendicular bisectors The circle touches the vertexes of the triangle

  21. Circumscribed Circle

  22. Where will this be used? Architectural design Surveying Crafts

  23. Where will this be used?

  24. Where is all of this used? http://www.clker.com/clipart-25627.html

  25. Conclusion Tools: Compass Straightedge Pencil

  26. Conclusion Angles and lines can be bisected with Circles Lines Points

  27. Work Cited http://www.daviddarling.info/encyclopedia/C/compasses.html http://www.theofficedealer.com/ACM45012-Westcott-45012-Shatter-proof-Ruler.html http://inefalon.info/staedtler- 55600-comfort-compass-set.php http://www.clker.com/clipart- 25627.html MMSTC

  28. Works Cited https://commons.wikimedia.org/wiki/File:Green_equilateral_triangle_point_up.svg http://en.wikipedia.org/wiki/Circumscribed_circle http://www.mathwords.com/i/inscribed_circle.htm

  29. ANY QUESTIONS?

  30. The Game! 2 players Whoever says the correct letter first wins- click “Answer” to get the correct answer Correct answers receive one point unless otherwise specified MMSTC

  31. Question 1 An angle is given, what is the first step in making it’s bisector? ( Where does the circle get placed?) Go To Diagram!!!

  32. A B C What’s the answer?

  33. Answer A

  34. Question 2 When two lines intersect, and a circle has been constructed, radiating from the intersection point, where does the compass needle go for the next step? Go To Diagram!!! MMSTC

  35. C A B What’s the answer?

  36. Answer C

  37. Question 3 Once one circle is constructed on the first circle’s intersection with the angle’s line, how big should you make the next one and where should it go? Go To Diagram!!!

  38. 4” A C B 8” 4” 4” What’s the answer?

  39. Answer B

  40. Question 4 When making a perpendicular bisector, where would you place the first circle? Go To Diagram!!!

  41. A B C What’s the answer?

  42. Answer A

  43. Question 5 After one circle has been created, beginning the creation of a perpendicular bisector, what would be the next step? Go To Diagram!!!

  44. A B C What’s the answer?

  45. Answer B

  46. Question 6 With two circles constructed, of equal size over both ends of the segment, what is the next construction to be made? Go To Diagram!!!

  47. A B C What’s the answer?

  48. Answer A

  49. Question 7 When creating an equilateral triangle, what is the first construction made on a segment? Go To Diagram!!!

  50. A B C What’s the answer?

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