Question

In a trapezium the lengths of its parallel sides are a and b the lengtlengths of the line joining the midpoints of its non parallel sides is

Answer 1

see figure, A trapezium ABCD is shown , where AD and BC is parallel sides of trapezium . length of AD = a and length of BC = b.
drawn line EF which is parallel to AD and BC , it joins the midpoint points of non parallel sides AB and DC .

now, from ∆ABC ,
E is the midpoint of AB and EO || BC
from basic proportionality theorem,
EO = 1/2 BC ........(1)

Similarly, from ∆ACD,
F is the midpoint of CD, and OF || AD
from basic proportionality theorem,
OF = 1/2 CD .........(2)

adding equations (1) and (2),

EO + OF = EF = 1/2 (BC+ CD)

or, EF = 1/2 (a + b)

hence, length of line joining the midpoints of its non parallel sides is half of the sum of length or parallel sides.

Answer 2

Answer:

Step-by-step explanation:

See figure, A trapezium ABCD is shown , where AD and BC is parallel sides of trapezium . length of AD = a and length of BC = b.

drawn line EF which is parallel to AD and BC , it joins the midpoint points of non parallel sides AB and DC .

now, from ∆ABC ,

E is the midpoint of AB and EO || BC

from basic proportionality theorem,

EO = 1/2 BC ........(1)

Similarly, from ∆ACD,

F is the midpoint of CD, and OF || AD

from basic proportionality theorem,

OF = 1/2 CD .........(2)

adding equations (1) and (2),

EO + OF = EF = 1/2 (BC+ CD)

or, EF = 1/2 (a + b)

hence, length of line joining the midpoints of its non parallel sides is half of the sum of length or parallel sides.