2014 · Q78
Let ABCD be a parallelogram. Let X and Y be the midpoints of the sides BC and AD respectively. Let M and N be the midpoints of the sides AB and CD respectively. Consider the following statements:
- 1The straight line MX cannot be parallel to NY.
- 2The straight lines AC, BD, XY and MN meet at a point.
Which of the above statements is/are correct?
Elementary MathematicsQuadrilaterals and Polygons
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
MX and NY are both parallel to AC (midpoint theorem in triangles ABC and ADC), so statement 1 is false; XY and MN both pass through the parallelogram's centre where the diagonals meet, so statement 2 is true.