Properties of Quadrilaterals

[finn.b14]

Hey guys,
I'm struggling to memorise all of the special quadrilateral rules such as the tests for parallelograms, rectangles, rhombus etc. (especially all the rules regarding diagonals!)
I was just wondering if...
a) should I be spending time rote learning all of these tests?
b) does anyone know any good tricks to remember them?
c) has anyone else come across the problem or am I studying too many rules?
Thanks heaps,
Finn 

[RuiAce]

Yeah, of course you need to know all the tests. Because you could very well be examined on any of them.

Having said that, it is a bit of a grind. To handle these, I started from the very bottom, at the parallelogram. I spent a few days just staring at the parallelogram and convincing myself that the following were true:
- Opp sides parallel
- Opp sides equal
- Opp angles equal
- Diagonals bisect
Notice how I looked for the properties first. After I knew the properties, I THEN moved onto the tests.
- If two pairs of opp sides parallel, then parallelogram
- If two pairs of opp sides equal, then parallelogram
- If one pair of opp sides are equal and parallel, then parallelogram
- If two pairs of opp angles equal, then parallelogram
- If diagonals bisect, then parallelogram

The point is, if you can convince yourself of the properties of the quadrilaterals, the tests then fall out of them. And the reason for starting with the parallelogram first is because everything builds on top of it.

A rectangle is just a parallelogram with the added properties that
- all angles are right angle
- diagonals are equal
and thus, so long as you have a parallelogram, if you can prove that
- either at least one angle is a right angle
- or if the two diagonals are equal
then you have a rectangle.

A rhombus is just a parallelogram with the added properties that
- ALL sides equal
- diagonals bisect at right angles (this is perhaps the hardest one to convince, and the only one I rote learnt)
and thus, so long as you have a parallelogram, if you can prove that
- either the diagonals meet at right angles
- or a pair of adjacent sides are equal
then you have a rhombus.

On top of that, the rectangle and rhombus are special in that they can be proven to exist without first checking for a parallelogram. But I find that you never need these.

If you prove that three angles are right angles, you have a rectangle.

If you prove that all four sides equal, you have a rhombus.

Finally, a square is just when you have a rectangle that's also a rhombus. Or a rhombus that's also a rectangle.

[LaraC]

I don't know if it helps you much but I find actually drawing the quadrilaterals and labelling the angles, sides etc that contribute to their properties or tests helps me to visualise it and remember them much better! not everyone is a visualiser though

[Sine]

I don't know if it helps you much but I find actually drawing the quadrilaterals and labelling the angles, sides etc that contribute to their properties or tests helps me to visualise it and remember them much better! not everyone is a visualiser though

yes drawing is definitely great!

Also if you want to double check any properties, make sure to draw out the shapes very big and also to scale. Doing this will minimise any sort of meausrement errors and since it's to scale you can test any properties. However this is definitlely a last ditch tactic if you only vaugely remember something during a test.