This chart provides answers and hints. Try to reason about the properties on your own and use hints only as the last resort. If the answer is YES or NO, make sure to write down a complete proof - hints only provide general ideas that you need to supplement it with all necessary details. If the answer is SOMETIMES, provide examples and counterexamples. For the area formulas, provide a clear justification.

Fill out each row from left to right (and top-down). Anything you prove can be used in the following boxes (to the right or above). This also means that to prove a property you can only assume things that are to the left of (or above) the box you are working on. You may also need to consult our minimal definitions of quadrilaterals and the guide for filling out this form.

	SIDES		ANGLES		DIAGONALS				AREA
	Parallel?	Congruent?	Congruent?	Relationship?	Congruent?	Bisecting?	Perpendicular?	Triangle Partition?
Kite	Sometimes	Yes – 2 pairs of adjacent sides	Yes – (at least) one pair of opposite angles. Can you specify which pair of opposite angles is congruent? HINT	Nothing remarkable Sometimes pairs of angles are supplementary	Sometimes	Yes – One diagonal always bisect the other HINT	Yes   HINT	Two pairs of congruent triangles. For concave kites, these triangles are fully or partially  "outside "the kite.	HINT
Trapezoid	Yes – (at least) one pair	Sometimes	Sometimes	2 pairs of adjacent supplementary angles HINT	Sometimes	Sometimes	Sometimes	One pair of triangles is similar. The other pair of triangles has the same area. HINT	HINT
Isosceles Trapezoid	Yes – (at least) one pair	Yes – one pair of opposite sides. Can you specify which pair? HINT	Yes – 2 pairs of angles adjacent to the bases.	2 pairs of adjacent supplementary angles HINT	Yes HINT	Sometimes	Sometimes	One pair of triangles is similar. The other pair of triangles is congruent. HINT
Parallelogram	Yes – two pairs	Yes – 2 pairs of opposite sides HINT	Yes – 2 pairs of opposite angles HINT	Adjacent angles are supplementary (Hint - see the box above)	Sometimes	Yes HINT	Sometimes	Two pairs of congruent triangles. HINT	HINT
Rhombus	Yes – two pairs HINT	Yes – all sides	Yes – 2 pairs of opposite angles HINT	Adjacent angles are supplementary (Hint - see the boxes above)	Sometimes	Yes (Hint - Can you apply hint from parallelograms to rhombi?)	Yes HINT or Can you apply the hint from kites to rhombi?	All triangles are congruent (Apply the previous hint (left box))
Rectangle	Yes – two pairs HINT	Yes – two pairs of sides HINT or try to apply the hint from Parallelograms	Yes – all angles HINT	Any two angles are supplementary (Hint - see the previous box)	Yes (Can you apply the hint from isosceles trapezoids?) HINT	Yes (Can you apply the hint from parallelograms?)	Sometimes	Two pairs of congruent triangles. (Can you apply the hint from parallelograms?)
Square	Yes – two pairs (Hint - see Observation 1 in the hint for rhombi)	Yes – all sides	Yes – all angles HINT	Any two angles are supplementary	Yes (Can you apply the hint from isoscleles trapezoids or rectangles?)	Yes (Can you apply the hint from parallelograms?)	Yes (Can you apply the hint from kites or rhombi?)	All triangles are congruent (Can you apply the hint from rhombi?)