properties
square
rect
rhomb
para
trap
kite
c-vex
c-cave
all sides congruent
yes

yes





opposite sides parallel
yes, both pairs
yes, both
yes, both
yes, both
only/at least 1 pair



diagonals bisect (at midpoints)
yes
yes
yes
yes

one diagonal is bisected when they cross


diagonals are perpendicular
yes

yes


yes, when they cross


diagonals are congruent
yes
yes






all angles are 90°
yes
yes






diagonals bisect the angles of the quadrilateral
yes

yes


one diagonal does


one diagonal is outside the quadrilateral







yes
the diagonals and the sides of the quadrilateral form 3 triangles







yes
the diagonals cross
yes
yes
yes
yes
yes

yes

adjacent angles add up to 180
yes, all pairs
yes, all
yes, all
yes
2 pairs add up to 180



2 pairs of adjacent sides are the same
yes

yes


yes


opposite sides are congruent
yes
yes
yes
yes




opposite angles are congruent
yes
yes
yes
yes

one pair is congruent



Questions to answer:
Can a trapezoid ever have perpendicular diagonals?  yes
Do all pairs of adjacent angles in a parallelogram add up to 180? 
Are the diagonals in a parallelogram always congruent?  (are they ever congruent?)
Does one of the diagonals of a parallelogram always bisect the angles it meets?
Does one of the diagonals of a kite always bisect the angles it meets?
What is the missing property in the table (hint--there is a shape that always has a property for one of its pairs of sides/angles that some other quadrilaterals have for both pairs of its sides/angles)