Problem: Each angle of a rectangle is trisected. The intersections of the pairs of trisectors adjacent to the same side always form:
Answer Choices:
A. a square
B. a rectangle
C. a parallelogram with unequal sides
D. a rhombus
E. a trapezium
Solution:
The diagonals of the quadrilateral formed lie along the two perpendicular lines joining the midpoints of the opposite sides of the rectangle. These diagonals are of different lengths, and they are perpendicular bisectors of each other. Therefore, the figure is a rhombus;
or
the sides of the quadrilateral can be proved equal by congruent triangles. Also, it can be proved that no interior angle is a right angle.