These are the conjectures and questions proposed by the class this term, ordered by date.

### January 13

Conjecture A (Pace): Let ABCD be a rhombus. Then angle BAC and BDC taken together make a right angle.

Conjecture B (Barker-Lewis): Let ABCD be a rhombus. If angle BAC is congruent to angle BDC, then ABCD is a square.

Conjecture C (class): It is possible to construct a rhombus which is not a square?

### January 18

Conjecture D (Reihman): Suppose that we have a diagram where A and D lie on the same side of line BC. Then angles ABC and BCD taken together make two right angles if and only if lines AB and CD are parallel.

### January 27

Question E: Is it possible to construct a kite which has no equilateral triangle? (The Van Donselaar examples all have triangle ABC as an equilateral triangle.)

Question F: What is an “interior angle?”

Question G: What is the “interior” of a polygon?

Question H: How do we differentiate between the “normal-looking” and the “odd-looking” kites? Is there some geometrical way of distinguishing these?

### January 30

Conjecture I: (Lewis) Given a segment AB and an angle XYZ, it is possible to construct a rhombus ABCD with angle ABD congruent to angle XYZ using a compass and straightedge.

### February 1

Question J: (Peters) Can we construct a kite with a given pair of sides and a given pair of opposite angles. More specifically: Given angles XYZ and $$\alpha \beta \gamma$$, and segments TJ and PQ, is it possible to construct a kite ABCD such that AB is congruent to TJ, BC is congruent to PQ, angle DAB is congruent to angle XYZ and angle DCB is congruent to angle $$\alpha \beta \gamma$$?

Lemma K: (Schmidt) Given segments AB and XY, one can construct triangle ABC so that BA and BC are both congruent to XY.

Contact Prof Hitchman
Theron J Hitchman
Department of Mathematics 0506
University of Nothern Iowa
Cedar Falls, IA 50613-0506
Other Contact Information
Office: 327 Wright Hall
Phone: 319-273-2646
email: theron.hitchman@uni.edu
Course Information
Class Meetings:
MWF 9am in WRT 105
Office Hours:
Use the link below to schedule a meeting during M-F 3-4:30pm.