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The line segment joining the mid -points of the diagonals of a trapezium is
  • a)
    Parallel to the non-parallel sides
  • b)
    Parallel to the parallel sides and equal ti the sum of the parallel sides.
  • c)
    Parallel to the parallel sides and equal to the difference of the parallel sides.
  • d)
    Parallel to the parallel sides, and , equal to half of the difference of the parallel sides.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The line segment joining the mid -points of the diagonals of a trapezi...
Understanding the Trapezium
A trapezium (or trapezoid) is a four-sided figure with at least one pair of parallel sides. Let's denote the parallel sides as 'a' and 'b', where 'a' is the longer side and 'b' is the shorter side.
Midpoints of the Diagonals
When we join the midpoints of the diagonals of a trapezium, we create a line segment. This segment has specific properties that relate to the trapezium's structure.
Properties of the Line Segment
- Parallelism: The line segment connecting the midpoints of the diagonals is always parallel to the parallel sides of the trapezium.
- Length: The length of this segment is equal to half of the difference of the lengths of the parallel sides. This means:
- If 'a' is the length of the longer parallel side and 'b' is the length of the shorter parallel side, then the length of the segment is given by (a - b)/2.
Conclusion
Therefore, the correct answer is option 'D': The line segment joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides and equal to half of the difference of the parallel sides. This property can be useful in various geometrical problems and proofs involving trapeziums.
Free Test
Community Answer
The line segment joining the mid -points of the diagonals of a trapezi...
P and Q are the mid-points of BD and AC respectively.

Applying mid-point theorem
PQ ∥ AB ∥ DC, and
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The line segment joining the mid -points of the diagonals of a trapezium isa)Parallel to the non-parallel sidesb)Parallel to the parallel sides and equal ti the sum of the parallel sides.c)Parallel to the parallel sides and equal to the difference of the parallel sides.d)Parallel to the parallel sides, and , equal to half of the difference of the parallel sides.Correct answer is option 'D'. Can you explain this answer?
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The line segment joining the mid -points of the diagonals of a trapezium isa)Parallel to the non-parallel sidesb)Parallel to the parallel sides and equal ti the sum of the parallel sides.c)Parallel to the parallel sides and equal to the difference of the parallel sides.d)Parallel to the parallel sides, and , equal to half of the difference of the parallel sides.Correct answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The line segment joining the mid -points of the diagonals of a trapezium isa)Parallel to the non-parallel sidesb)Parallel to the parallel sides and equal ti the sum of the parallel sides.c)Parallel to the parallel sides and equal to the difference of the parallel sides.d)Parallel to the parallel sides, and , equal to half of the difference of the parallel sides.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line segment joining the mid -points of the diagonals of a trapezium isa)Parallel to the non-parallel sidesb)Parallel to the parallel sides and equal ti the sum of the parallel sides.c)Parallel to the parallel sides and equal to the difference of the parallel sides.d)Parallel to the parallel sides, and , equal to half of the difference of the parallel sides.Correct answer is option 'D'. Can you explain this answer?.
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