Question

In which type of trapezoid do the diagonals bisect one another?

right trapezoid
isosceles trapezoid
any trapezoid
no trapezoid

Answer 1

Hmm - helps to visualise? - any idea which option now?

Answer 2

is it no trapezoid?

Answer 3

ya.....

Answer 4

No, never........ Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. But this is a contradiction since the respective bases of the triangles, forming the top and bottom of the trapezoid are, of course, not equal. Therefore, the triangles cannot be congruent. Hence, we have given proof by contradiction that diagonals in a trapezoid cannot bisect each other.

Answer 5

@tornjeansxo

Answer 6

Yes it is 'no trapezoid' - also Nitz has provided a pretty good explanation above.