11 Plus Exams Forum

Please may I have some advice on Trapeziums?
I refer to Q2 on the 'shapes' section of The Tutors 11+ Maths Volume 1 CD rom.
The 'correct'? answer is D (four shapes), however this has caused confusion in our house. Which is the fourth shape? Shape E is a five sided shape and shape C is a parallelogram (it may be a rhombus - my eyes are not so good anymore!)
I understand a trapezium to be a quadrilateral with one pair of parallel sides. I know it may also have (at times) 2 pairs of equal opposite sides, 2 pairs of equal adjacent angles, 1 line of symmetry etc. Am I going mad?
Please, if anyone has this CD rom, could you check for me and tell me where I'm going wrong?
Worth noting also is that question 12 and 22 on the same CD rom doesn't consider a parallelogram (albeit tipped on it's side - upright..) This merely adds to my confusion as that would imply the 5 sided shape is the fourth shape for question two - but it's not a quadrilateral...
I fear I can no longer see the wood through the trees!
Please help!
Belinda

Hi Belinda

I do not have access to the question sets immediately, I should be able to get back to you with an explanation tomorrow.

Regards

Mike

Thank you Mike,
Trapeziums seem to crop up more often than other shapes and my daughter is sitting the Medway tests next week! We both thought we knew what a trapezium was - now we're not so sure! (please let it be a misprint!)
Belinda

Hi Belinda

I have checked the original document that was sent to elevenplusexams.co.uk for input and the corrct answer is "C" not "D". Therefore if you take "C", 3 as being correct then hopefully there is no further confusion over trapeziums.

I will check with the programmers to find out if the incorrect answer exists on current CDs, if it does we can get it corrected quickly, then anyone with the CD or download will be able to get an upgrade.

Regards

Mike

Thank you very much Mike,
Belinda

Any parallelogram is definitely still a trapezium.

The definition of a trapezium is that it is a quadrilateral with a pair of parallel sides. This still applies to shapes that have 2 such pairs. A parallelogram is a special case of a trapezium. This does not mean that it ceases to be a trapezium, just as a square is still a rectangle and a rhombus is also a kite. In fact a square is a rectangle, and a parallelogram , and a rhombus and a kite and a trapezium.

Just because special cases have extra properties, it does not mean that they cease belonging to more general sets of shapes.

In general in mathematical definitions when the indefinite article is used, that still allows for more than one instance. So a parallelogram is still a trapezium because it is possible to point to a pair of parallel sides. Just because you can do it in two ways, does not mean you cannot do it at all. "A pair" means just that, not "one and only one pair".

Similarly a rhombus is still a kite, and a rectangle is also a parallelogram.

So the original Tutors answer appears to be correct.

I write as someone with a Mathematics degree.
MR

Here is a link http://eprints.soton.ac.uk/41247/01/Fuj ... 0_2006.pdf
to a report on understanding of basic geometry amongst primary school teachers in Scotland.
The sad conclusion is that only 8.7% correctly knew that a square, a rectangle and a parallelogram are in fact all special cases of trapezia.
This contrast to 73% in Japan.
People are perhaps fooled by picture which show the general case (only one pair of parallel sides), and then think that special cases like a rectangle are not also examples of the more general trapezium.
Think of it as a hierarchy with the most special case (square) at the top, and more general cases going down.
Saying a parallelogram is not a trapezium is like saying a square is not a quadrilateral.
Unfortunately I'm not sure if all the examiners really understand the proper definitions either.

So the hierarchy is
Square
Rectangle Rhombus
Parallelogram Kite
Trapezium
Quadrilateral

Also a rhombus is a special case of a parallelogram.
MR

This is also something that drives me to distraction!! My child [when in reception] came home to tell me that a rectangle had two long sides and two short sides ...

Also why are ploygons e.g. pentagons always shown with equal sides in primary resources ...

mgr, does this mean that, when my son's homework was marked as wrong because he'd named a given shape as a parallelogram instead of the published answer of rhombus, he was actually right?

(Not meaning to offend anyone)

.