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The Parallel sides of a trapezium are ‘a’ and ‘b’ res. The line joining the mid-points of its non-parallel sides will be
  • a)
    1/2 (a+b)
  • b)
    2ab/(a+b)
  • c)
    1/2 (a-b)
  • d)
    None of These
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The Parallel sides of a trapezium are ‘a’ and ‘b&rsq...
Given: The parallel sides (
A
B
 and 
C
D
) of the given trapezium are of length 
a
 and 
b
.
A line joining the midpoints of the non-parallel sides of a trapezium will always be parallel to the parallel sides of the trapezium
i.e. 
E
F
A
B
C
D
In 
A
D
B
,
 we have
E
 is the midpoint of 
A
D
,
 and 
E
G
A
B
 [
E
F
A
B
]

By Converse of midpoint theorem, 
G
 will midpoint of 
B
D
.
 and 
E
G
=
1
2
A
B
i.e. 
E
G
=
1
2
b
(
i
)
In 
D
B
C
,
 we have
G
 is the midpoint of 
B
D
 and 
F
 is the midpoint of 
B
C
.
By midpoint theorem, 
G
F
C
D
,
 and 
G
F
=
1
2
C
D
i.e. 
G
F
=
1
2
a
(
i
i
)
On adding eq.(i) and (ii), we get
E
G
+
G
F
=
1
2
b
+
1
2
a
E
F
=
1
2
(
a
+
b
)
Hence,the line joining the midpoints of its nonparallel sides is equal to 
1
2
(
a
+
b
)
.
Free Test
Community Answer
The Parallel sides of a trapezium are ‘a’ and ‘b&rsq...
1/2 (a+b),option 'A'.
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The Parallel sides of a trapezium are ‘a’ and ‘b’ res. The line joining the mid-points of its non-parallel sides will bea)1/2 (a+b)b)2ab/(a+b)c)1/2 (a-b)d)None of TheseCorrect answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The Parallel sides of a trapezium are ‘a’ and ‘b’ res. The line joining the mid-points of its non-parallel sides will bea)1/2 (a+b)b)2ab/(a+b)c)1/2 (a-b)d)None of TheseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Parallel sides of a trapezium are ‘a’ and ‘b’ res. The line joining the mid-points of its non-parallel sides will bea)1/2 (a+b)b)2ab/(a+b)c)1/2 (a-b)d)None of TheseCorrect answer is option 'A'. Can you explain this answer?.
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