Class 9 Exam > Class 9 Questions > The line segment joining the mid -points of t...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
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
FREE
| Start 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
Applying mid-point theorem
PQ ∥ AB ∥ DC, and
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
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?
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup