# isoscels trapezium

• Nov 6th 2009, 09:21 PM
jashansinghal
isoscels trapezium
prove that in an isosceles trapezium
[sum of parallel sides] x [sum of non parallel sides]= product of diagnols
• Nov 7th 2009, 02:09 AM
Bacterius
A isosceles trapezium named ABCD has just been created from nothing. The sides (AB) and (CD) are parallel. Therefore, we have :

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

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

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

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 ?
• Nov 7th 2009, 08:24 PM
jashansinghal
sorry,I am not able to understand
• Nov 7th 2009, 08:37 PM
Bacterius
What don't you understand ?
• Nov 7th 2009, 08:48 PM
jashansinghal
what do you mean to say?
• Nov 7th 2009, 08:53 PM
Bacterius
Quote:

Originally Posted by jashansinghal
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.
• Nov 7th 2009, 09:02 PM
jashansinghal
• Nov 7th 2009, 09:05 PM
Wilmer
Quote:

Originally Posted by jashansinghal
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
• Nov 16th 2009, 07:29 PM
jashansinghal
ya...it should be this...but how to proceed
• Nov 16th 2009, 08:11 PM
Bacterius
Quote:

Originally Posted by jashansinghal
ya...it should be this...but how to proceed

Wait wait ... can you give the exact terms of the question ? Otherwise it's useless.
• Nov 17th 2009, 06:49 AM
jashansinghal
prove that in an isosceles trapezium
[sum of parallel sides] x [sum of non parallel sides]= product of diagnols
• Nov 17th 2009, 03:12 PM
Bacterius
Quote:

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

Are you just solving for solving or what ?
• Nov 18th 2009, 07:54 AM
jashansinghal
• Nov 21st 2009, 02:16 PM
aidan
stated
Quote:

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

Quote:

Originally Posted by Bacterius
Wait wait ... can you give the exact terms of the question ?

restated
Quote:

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

...
a counterexample: