Thread: isoscels trapezium

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

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



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



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 ?

sorry,I am not able to understand

What don't you understand ?

what do you mean to say?

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.

please help me

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

ya...it should be this...but how to proceed

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.

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

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 ?

please help me....can you do first few steps

stated

Originally Posted by jashansinghal

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

asked for clarification

Originally Posted by Bacterius

Wait wait ... can you give the exact terms of the question ?

restated

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: