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: Understanding the Question:
This question is from Geometry, specifically concerning the properties of quadrilaterals.
We need to identify which of the given quadrilaterals does not have the property that its diagonals bisect each other.

Step 2: Key Formula or Approach:
We recall the defining properties of diagonals for different classes of quadrilaterals:
1. In any parallelogram, the diagonals always bisect each other.
2. Special types of parallelograms (Rectangle, Rhombus, Square) inherit this property.
3. In a general trapezium, the diagonals do not bisect each other.

Step 3: Detailed Explanation:
Let us analyze the properties of each option:
- Parallelogram (Option C): By definition, a parallelogram has opposite sides parallel and equal. A fundamental theorem states that the diagonals of a parallelogram bisect each other.
- Rhombus (Option B): A rhombus is a special parallelogram with all four sides equal. Since it is a parallelogram, its diagonals bisect each other (and they do so at right angles).
- Rectangle (Option D): A rectangle is a special parallelogram with four right angles. Since it is a parallelogram, its diagonals bisect each other (and they are equal in length).
- Trapezium (Option A): A trapezium is a quadrilateral with only one pair of parallel sides. Because it is not a parallelogram, its diagonals do not bisect each other. Instead, they divide each other in the same ratio.

Step 4: Final Answer:
The quadrilateral for which the diagonals do not bisect each other is the Trapezium.