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Drawing #1Geometry Drawing AssignmentThe purpose of this exercise is to give the student practice in the construction of a perpendicular line to a point, the construction of a perpendicular bisector of a line segment, to measure and mark lengths with accuracy, to graphically prove that the Pythagorean Theorem is accurate, to construct a circle which circumscribes a triangle, and to bisect angles.Click HERE to hear the audio instructions for drawing #1
Scroll down to see the directions for this drawing exercise.1. Orient your piece of 8 1/2 x 11 inch plain paper so it is in landscape orientation (sideways).2. Sketch a grid in the upper left corner about 2 inches by 2 inches which you will use to enter the numbers 1 through 5 along with their square roots and squares.3. Enter your name at the top right of the page.4. Draw a horizontal line from left to right at the bottom of the page about 1 inch up.5. Mark a point at about the middle of this horizontal line. No need to measure.6. Use a compass to scribe arcs to the right and left of this midpoint mark (about three inches will be fine).7. Reposition the compass so you can now scribe arcs high above the midpoint mark (say five inches). This is to be done from each of the two arc marks. Then draw the straight line which goes through this intersection and runs to the midpoint mark. (This is a perpendicular line drawn to a point).8. Add a mark at 3 inches to the left of the midpoint mark on the horizontal line. It describes the length of this line segment which is the bottom of the triangle being drawn.9. Add a mark 4 inches up the perpendicular line from the midpoint. Accuracy is important in this measurement. This will be one of the legs of the 3-4-5 right triangle being drawn.10. Draw the hypotenuse with a straight edge from endpoints of these two line segments. Measure the length. Five inches is correct. This drawing graphically demonstrated that for a 3-4-5 inch triangle, the Pythagorean Theorem is correct. (Not that there was ever any doubt).11. Construct a perpendicular bisector for each of the sides of this triangle. This is done with a compass. From each end on one of the line segments, scribe an arc where the arc would intersect the perpendicular line you can imagine for it. Do the same for both sides of the line, and in both directions. Then draw the straight line which passes through both of these arc intersections.12. Do the same for all three sides of the triangle.13, Notice these perpendicular bisectors pass through the same point which is the midpoint of the hypotenuse. Use this midpoint as the center for a circle which you now draw with a compass. The circumference of this circle you will draw will pass through all three corners of the triangle.14. Next, on the right side of the drawing, see the right angle. Now draw the bisector of the 90 degree angle in the following way. With a compass point on the 90 degree angle intersection, scribe out an arc mark on each of the lines to the top and to the right.15. Reposition the compass to now scribe arcs out and away from the 90 degree point from both of the intersections of these arc marks. Where the arcs intersect, draw a line which passes through this intersection and runs to the 90 degree corner. This bisects the 90 degree angle into two 45 degree angles.16. Repeat this process for each of the 45 degree angles.17. This concludes the drawing exercise.Have a nice day. Cheers:>)David U. Larson
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Prepared 2005-Revised 2006
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