Question

For which of the following figures, diagonals don't bisect each other?

• A. Trapezium
• B. Rhombus
• C. Parallelogram
• D. Rectangle

Hint:

Remember that Rectangle, Rhombus, and Square are all subsets of Parallelograms.
Since they share basic parallelogram properties, if one of them has bisecting diagonals, they all must.
This leaves Trapezium as the odd one out.

Answer 1

The Correct Option is A

Step 1: Recall why diagonals bisect each other in a parallelogram.
A parallelogram, and every special case of it such as a rectangle or a rhombus, has two pairs of parallel sides. This built in symmetry is exactly what forces the diagonals to cross at their common midpoint.
Step 2: See what happens when that symmetry is missing.
A trapezium has only one pair of parallel sides, not two. Picture a trapezium with a short parallel side and a long parallel side, if you draw both diagonals, the point where they cross divides each diagonal in the ratio of the two parallel sides, not in a 1:1 ratio. So the crossing point is not the midpoint of either diagonal.
Step 3: Conclude.
Rhombus, parallelogram and rectangle all keep the bisecting property, only the trapezium loses it. \[ \boxed{\text{Trapezium}} \]