1) Perpendicular bisector 2) Angle bisector of a line segment
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1 1) Perpendicular bisector 2) ngle bisector of a line segment 3) line parallel to a given line through a point not on the line by copying a corresponding angle. 1
2 line perpendicular to a given line through a point: 4) not on the line 5) on the line In both cases, you must place the needle of your compass on the point and make a segment to bisect. 6) Construct parallelogram G, by translating vector G to. G G First, copy the length of G at Next, measure G (tail to tail) and copy at (head to head) 2
3 6) Construct parallelogram G, by translating vector G to. G G Draw vector. Finish parallelogram. 7) Construct the line of reflection. C C' ' Connect any point with its image and construct the perpendicular bisector. 3
4 8) Reflect over the given line. Place the needle of the compass at, and make an arc that intersects the line in 2 places. hen use the same radius, and place the needle of the compass at each endpoint to get an intersection. asically, we are constructing an isosceles triangle at, and then copying it over the line to. his creates a rhombus. 8) Reflect over the given line. ' ' Repeat process from. ' Repeat process from. 4
5 8) Reflect over the given line. ' ' ' ' Connect image points the same way that is connected. 9) Find the center of rotation. C C' C C' ' it'; ' Construct the perpendicilar bisector of any point and its image. Complete a second perpendicular bisector of a point and its image. Where they intersect is the center. 5
6 10) Measure the angle of rotation. C C' nearest 10 degrees Connect the center with any point and then the center with the image pair. Measure with a protractor. ' cw ) Dilate triangle YZ a scale factor of 2 by SS using vertex. Write a similarity statement for the triangles. Y Z Since we must use angle, extend the rays of that angle. Y Y' Z Now measure Y and scale 2 "units" from 6
7 11) Dilate triangle YZ a scale factor of 2 by SS using vertex. Write a similarity statement for the triangles. Y Y' Y Y' Z Z Z' Now measure Z and scale 2 "units" from Connect Y' to Z' Z' 12) Construct a square inside circle. Draw any diameter (through the center). Construct the Connect intersections on perpendicular bisector circle to make square. Parallelogram: ll radii of the same circle therefore diagonals bisect each other Rectangle: construction yields another diameter which prove diagonals. Rhombus: Perpendicular diagonals Parallelogram + Rectangle + Rhombus = Square 7
8 13) Find the center of the circle. Draw any chord. C Construct the perpendicular bisector of the chord. his yields a diameter. Construct the perpendicular bisector of the diameter which passes through the center. 14) Construct a hexagon inside circle. Put the needle of the compass at and measure the radius of the circle. Put the needle of the compass anywhere on the circumference of the circle & make an arc that intersects the circle. "Piggy back" all the way around. Connect all intersections of arcs with circumference of circle. 8
9 equidistant to each of the given points. Connect any two points and construct the perpendicular bisector. Connect another pair of points & construct the perpendicular bisector. Where they intersect is the circumcenter. he circumcenter is the point which is equidistant from each of three points that are not on the same line (would make a triangle). he circle proves the equidistance. May 31 7:15 PM 9
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