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Classic Constructions • Ryan Caliguri – WMHS • Jeffrey Wainz - WMHS 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 G.SR.07.02 • Terminology • Informal justifications G.SR.07.02 • Basic Geometric Constructions – – – – – Perpendicular Bisector Equilateral Triangle Angle Bisector Inscribed Circle Circumscribed Circle Terminology Compass: an adjustable device used to construct circles Straight Edge: any tool that is used to draw straight lines during constructions Terminology Bisector: line that divides a segment or angle into two equal halves Perpendicular: lines that intersect at 90 degree angles Terminology Equilateral Triangle: triangle with 3 congruent sides and angles Circumscribed Circle: a circle drawn around a triangle Terminology Vertex: the point where two lines intersect to form an angle Inscribed Circle: a circle drawn inside of a triangle Terminology Line: a figure that goes on forever in 2 directions Line Segment: a line with a defined length 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 Perpendicular Bisectors • Cuts a line in half • New line is perpendicular to the original segment Constructing a Perpendicular Bisector Angle Bisectors • Cuts an angle in half • Two new created angles are congruent Constructing Angle Bisectors Equilateral Triangle • A triangle with sides of exactly the same side • All angles are 60 degrees Constructing Equilateral Triangles Inscribed Circle • Creates a circle using angle bisectors • The circle touches all three sides of the triangle Inscribed Circle • Prerequisites – Angle bisectors – Perpendicular lines through a point Inscribed Circle Circumscribed Circle • Creates a circle using perpendicular bisectors • The circle touches the vertexes of the triangle Circumscribed Circle Where will this be used? • Architectural design • Surveying • Crafts Where will this be used? Where is all of this used? http://www.clker.com/clipart-25627.html Conclusion Tools: • Compass • Straightedge • Pencil Conclusion • Angles and lines can be bisected with – Circles – Lines – Points Work Cited • http://www.daviddarling.info/ency clopedia/C/compasses.html • http://www.theofficedealer.com/A CM45012-Westcott-45012-Shatterproof-Ruler.html • http://inefalon.info/staedtler55600-comfort-compass-set.php • http://www.clker.com/clipart25627.html MMSTC Works Cited • https://commons.wikimedia.org/wi ki/File:Green_equilateral_triangle _point_up.svg • http://en.wikipedia.org/wiki/Circu mscribed_circle • http://www.mathwords.com/i/inscr ibed_circle.htm ANY QUESTIONS? 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 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!!! A B C What’s the answer? Answer 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 C A B What’s the answer? Answer 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!!! 4” C A B 4” 4” What’s the answer? 8” Answer Question 4 • When making a perpendicular bisector, where would you place the first circle? Go To Diagram!!! A B C What’s the answer? Answer Question 5 • After one circle has been created, beginning the creation of a perpendicular bisector, what would be the next step? Go To Diagram!!! A B C What’s the answer? Answer 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!!! B A C What’s the answer? Answer Question 7 • When creating an equilateral triangle, what is the first construction made on a segment? Go To Diagram!!! A B C What’s the answer? Answer Question 8 • In the creation of an equilateral triangle, after a circle is created around a given point, what size should the next circle be? Go To Diagram!!! B 4” A C 2” 4” 8” What’s the answer? Answer Question 9 • With two points of an equilateral triangle discovered, where does the third go? Go To Diagram!!! B C A What’s the answer? Answer