In the five constructions below, use a separate sheet of paper for each problem, and give yourself plenty of room to work. Use only one side of each sheet of paper. Use a dark pencil or pen. Do not erase (except for mistakes) but show all construction lines so that I can see what you did. That is, where you put the point of the compass and what arcs or lines you drew. Label the parts of your diagram carefully. Include a step by step description of your construction at the end of each construction.
See me for help or hints. You may get other help, and work with other students is encouraged, but hand in your own work which is not a copy of someone elseŐs.
Buy a compass if you
donŐt already have access to one. I have ten sets of rulers and compasses in my
office. If you want to drop by and borrow a set, they are there to use. Please
restrict yourselves to one set per group of students who plan to work together.
1.EuclidŐs first proposition (Theorem) states that, given any straight line segment, an equilateral triangle exists having that segment as one of its three congruent sides. Draw a straight line segment a few inches long, and construct the predicted triangle. Use only a compass and a straight edge. You canŐt use the measuring marks on the ruler.
2. Draw any triangle that has three different lengths for its three sides. Use your compass and straight edge to make a congruent copy of it.
3. Draw any angle, as long as it is not a right angle. Use your compass and straight edge to make a congruent angle.
4. Draw a line L and
a pint P not on the line L. Construct a line which passes through P and is parallel to L.
5. Draw three large triangles that look different from each other to you, one each on separate sheets of paper. For the first triangle, construct the three perpendicular bisectors of the three sides. For the second, construct the three angles bisectors of the three angles of the triangle, for the third, construct the three medians. On each page write the appropriate definition of perpendicular bisector, angle bisector or median. On each page the three lines you drew should intersect in one point, of you extend the lines far enough. The intersection point may be inside or outside of the triangle.