| Some of these descriptions aren't complete for what you're trying to describe. For example, "Diagonals are congruent" isn't enough to characterize a rectangle—you have to say that the diagonals bisect each other too. You apparently know this, because you have "Diagonals are congruent and bisect each other" as a separate clue for rectangles, and you have "Diagonals congruent, but only one pair of opposite sides is parallel" as a clue for isosceles trapezoid (and clearly isosceles trapezoids are not rectangles, even though their diagonals are congruent). Similarly, "Diagonals are perpendicular" is not enough to describe a rhombus—if I draw two perpendicular lines that cross at some random point, then in general I'm not going to get a rhombus. "Diagonals are perpendicular" describes a class of shapes called "orthodiagonal quadrilaterals," which includes rhombuses, kites, and some shapes that are neither of these. |