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