RECTANGLE

ah, this post is taking reference to MATHS TYS, 2004 PAPER 1, QUESTION 3

the information derived is that the diagonals of a parallelogram is equal, and we're supposed to deduce the shape of the quadrilateral.

basically, the answers proposed are rhombus, square and rectangle.

let me give you all reasons why is the answer a RECTANGLE, and not square or rhombus.

rhombus DO NOT have equal diagonals.(refer to http://en.wikipedia.org/wiki/Rhombus#Area)
the fact that they write D1XD2 refers to the fact that the diagonals are NOT equal.
hence, rhombus is NOT the answer.

square is a subset of a rhombus(when the angle between the sides are 90), and also a subset of a rectangle(when the sides of the rectangle are equal). Hence, when you say the answer is a square, you may be right, but you may also be wrong. simply because you don't know the sides of quadrilateral given.

so why rectangle?
firstly, because it's not a rhombus. secondly, when you say RECTANGLE, which is a superset of a square, you are including SQUARE in your answer. hence, if the sides are equal, tada, you're right. you get a square. but when the sides are not equal, you're not wrong! simply because you proposed the shape to be a rectangle, and not a square where the sides are supposed to be equal!

mr pats (my maths teacher) spent like 30mins thinking about this question in class, trying to derieve a proof for the fact that it's a rectangle. also, he said that rhombus' diagonals are equal, which is not true based on the evidence cited above. hence, he was unable to conclude the answer for the question, and spent a WHOLE 30mins(or more, i think) thinking of the answer. in the end, ONE WHOLE tutorial go through 2 question. lol.

anyway, i'm halfway through my tys 2006 paper1. i'm so lazy to do la. and i HATE studying at home. i got nowhere to write, nowhere to do my work. so i'm doing my work on my bed, which normally induce sleepiness into me. and this may be part of the reason why i'm not going to finish the paper today. also, because there are still a few BIGGER questions in 2004 paper 1 which he haven't go through, i doubt he can even make it to the 2006 paper by tmr. so, taking probability, i think the chances are low, hence resulting my my cost-benefit decision. (cost takes into account potential cost and actual cost, multiplied by their probability)

so, I'M OFF TO BED ALR. DAMN TIRED. 4am liao, sleep 2 hrs have to wake up. lol. anyway, first period tmr is PE. SHIOK, PLAY MY BELOVED BASKETBALL TMR =D