Possible Questions for Quiz 1

Note: For all proofs that say "if and only if," both directions must be proved. Make it clear which direction you are proving; don't mix them up.

• Prove that a point C is on the perpendicular bisector of segment AB if and only if AC = BC.

We call this statement above the Locus Property of Perpendicular Bisectors. A locus is a set. This says the set of points for which AC = BC is the same as the line that is the perpendicular bisector.

• Prove the Triangle Inequality (page 18).

• Prove that ABCD is a parallelogram if and only if AB = CD and AD = BC. (See p. 25)

• Prove that ABCD is a parallelogram if and only if the diagonals bisect each other. (See p. 25)

• Prove that for a quadrilateral ABCD is a rhombus if and only if the diagonals bisect each other and are perpendicular.

Possible Constructions for Quiz 1

Note: If you have a copy of Birkhoff and Beatley, there is a nice chapter on constructions in that book also.

• Make any construction in Chapter 1.

• Given a segment AB, construct points C and D so that ABCD is a square. (Note: you are starting with a side of the square.)

• Given a line AB and a point C, construct a point D so that line CD is parallel to AB. (Hint: You can do this is by copying an angle (p. 19). Another way is to construct D so that ABCD is a parallelogram, using one of the properties equivalent to the definition of a parallelogram.

• Construct the circumcircle of a triangle.