isoscels trapezium

jashansinghal · #1 $Old$ November 6th, 2009, 11:21 PM

prove that in an isosceles trapezium
[sum of parallel sides] x [sum of non parallel sides]= product of diagnols

Bacterius · #2 $Old$ November 7th, 2009, 04:09 AM

A isosceles trapezium named ABCD has just been created from nothing. The sides (AB) and (CD) are parallel. Therefore, we have :

$(AB + CD)(BC + AD) = AC \times BD$

Note that BC = AD (since the trapezium is isosceles)
Therefore :

$(AB + CD)(2BC) = AC \times BD$

Now draw such a trapezium and think of as many useful things as you can : Thales, Pythagoras, Trigonometry, Vectors, anything. Then try putting it all together to substitute formulas into the original equation, so as to prove that the sum of the parallel sides times the sum of the non-parallel sides equals the product of the diagonals. Does it help ?

jashansinghal · #3 $Old$ November 7th, 2009, 10:24 PM

sorry,I am not able to understand

Bacterius · #4 $Old$ November 7th, 2009, 10:37 PM

What don't you understand ?

jashansinghal · #5 $Old$ November 7th, 2009, 10:48 PM

what do you mean to say?

Bacterius · #6 $Old$ November 7th, 2009, 10:53 PM

Quote:

Originally Posted by jashansinghal $View Post$

what do you mean to say?

I'm trying to give you a hint on how to do it. I won't do it for you.

jashansinghal · #7 $Old$ November 7th, 2009, 11:02 PM

please help me

Wilmer · #8 $Old$ November 7th, 2009, 11:05 PM

Quote:

Originally Posted by jashansinghal $View Post$

prove that in an isosceles trapezium
[sum of parallel sides] x [sum of non parallel sides]= product of diagnols

Shouldn't that be:
[product of parallel sides] + [product of non parallel sides] = product of diagonals

In other words, if d = diagonal, a and b = parallel sides, c = non parallel sides:
prove that d^2 = ab + c^2