# Thread: isoscels trapezium

1. ## 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 :

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

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 ?

3. sorry,I am not able to understand

4. What don't you understand ?

5. what do you mean to say?

6. 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.

8. 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

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

10. 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.

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

12. 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 ?

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