Answers to Quadrilateral
thinking (according to the author S. Kim)
2. D and J. A parallelogram always has opposite angles of
equal measure.
3. The two types of quadrilaterals that can be concave are C
(Kite), and L (one pair of opposite sides of equal length).
4. K (one pair of 90-degree opposite angles) is a subclass of
B (Cyclic quadrilateral: All corners lie on a single circle), which is in turn
a subclass of A (Convex). As shown in the diagram below, any quadrilateral of
class K is composed of two right triangles, and the right-angle vertex of a
right triangle always lies on the semicircle whose diameter is the hypotenuse
of the right triangle.
5. H (Square), G (Rhombus) or F (Rectangle), D
(Parallelogram), I (Trapezoid), A (Convex), E (Quadrilateral). Can you find any
other solutions?
6. C (Kite), I (Trapezoid), L (one pair of opposite sides of
equal length), and K (one pair of opposite angles both 90 degrees) or B
(Cyclic).
Note: for problem 5 to work we have to use the definition that a trapezoid has at
least one pair of parallel sides (and
possibly two pairs of parallel sides!)
So it comes down to which definition is used!