MATH 141 InClass Exercise on Constructions

Perform each of the following constructions using straight edge and compass. Hand in one of each construction per group. Also for each construction list every use of the compass by naming the center and radius and each use of the straight edge by giving the two points that determine the line. (Label the points you use at each step.)

1. Draw a straight line about 5 inches long in the center of a blank sheet of paper. Construct an equilateral triangle on that segment. Then bisect each side of the triangle. Use the three midpoints to draw four smaller equilateral triangles inside the original one.

2. Draw a straight line about 4 inches long in the center of a blank sheet of paper. Construct a square on that segment. Then circumscribe a circle about the square. That is, construct a circle that passes through the four vertices of the square. (Hint: What does the center of that circle have to be?)

3. a) Draw a segment about 2 inches long in the center of a blank sheet of paper. Call it AB. Construct a right triangle whose legs are of length AB and length 2AB. Label the right triangle so that the right angle is at A and such that AC is the longer leg. Find the point D on BC, the hypotenuse, such that AB = BD.

b) On a new sheet of paper construct an isosceles triangle whose equal sides are of length AC from the previous right triangle and whose base is of length CD. Draw circles of radius CD from the three vertices of this triangle. You should then be able to connect five points to form a regular pentagon.