Assignment 1C (Due Monday, 10/6)

Lab Follow-up

Carry out these 3 constructions. Leave the construction marks showing. On the side, write an outline of the steps you have taken (just the major steps).

1.5 Construct a square

Construct with straightedge and compass a square ABCD with A and B given below.  Note, since the square is ABCD, this means AB is a side of the square. Describe briefly the steps in your construction. (You can just describe; you need not justify the steps.)

1.6 Copy a triangle.

Construct a triangle DEF that is congruent to triangle ABC, given A, B, C and D below. The point E should be on the given ray. Describe briefly the steps in your construction. (You can just describe; you need not justify the steps.)

1.7 Bisect an angle

• Draw an angle ABC and bisect it with a straightedge and compass. Describe briefly the steps in your construction.
• Explain why this construction works by citing theorem(s) that you have proved during the week.

1.8 Concurrence of perpendicular bisectors of a triangle

• Draw a general* triangle ABC and construct with straightedge and compass the perpendicular bisectors of the sides.
• Prove that the 3 perpendicular bisectors are concurrent at a point O.
• Construct the circle with center O through A.
• Explain why the circle with center O through A also passes through B and through C.

*General is a somewhat ill-defined term, but referring to an example, it means not special, so it should not be isosceles, equilateral, having a right angle or any other "special" angle such as 60 degrees. It means what one might call a "random" triangle if one could give a good definition of random.