Question

The sum of 2 adjacent angles of a trapezium is 90 The length of two parallel sides are 'a' and 'b' respectively. Then prove that length of the line segment joining mid-points of two parallel sides is 1/2*mod(a-b)

Answer 1

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Answer 2

Answer:

in the figure M and N are mid points

NE=b/2-(b-(a+X))

=a+x-b/2

OM=a/2-NE

a/2-(a+x-b/2)

OM=(b-a)/2-x

applying tan alpha and tan 90-alpha

we get

h^2=x(b-a)-x^2

again in triangle OMN applying Pythagoras theorem

we get d^2=((b-a)/2-x)^2+x(b-a)-x^2

d=|a-b|/2