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ABCD is a parallelogram and X, Y are the mid-points of sides AB and CD respectively. Then quadrilateral AXCY is a :
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- parallelogram
- rhombus
- square
- rectangle
- None of these
Correct Option: A
ABCD is a parallelogram and AXCY is a quadrilateral .
Since X and Y are the mid-points of AB and DC respectively.
| ∴ AX = | 1 | AB and CY = | 1 | DC |
| 2 | 2 |
| But ∴ AB = DC ⇒ | 1 | AB = | 1 | DC ⇒ AX = CY |
| 2 | 2 |
Also, AB || DC [∴ ABCD is a parallelogram]
⇒ AX || YC
Thus, in quadrilateral AXCY,
AX || YC and AX = YC
Hence, quadrilateral AXCY is a parallelogram.In which the opposite sides are equal and parallel.
