Question

let ABCD be a trapezium in which AB||CD and let E is the midpoint of AD.If G is a point on BC such that EG||DC.prove that EG=1/2(AB+DC)​

Answer 1

Answer:

I ll show it through an attachment

Step-by-step explanation:

it is a tricky diagram but this is the correct one.

we have,

AB//CD

but CD//EG (given)

EG//AB then GM//AB

In triangle ABC, GM//AB and G is the mid point of AC. then M is the mid point of AC (THEOREM:THE LINE DRAWN THROUGH THE MID POINT OF ONE SIDE OF A ∆ // TO ANOTHER SIDE BISECTS THE THIRD SIDE)

GM=1/2 AB --------1

(THEOREM: THE line joining the mid point of two sides of ∆ is // to the third side and is 1/2 of its length)

Similarly in triangle ABD

EM= 1/2 CD-------2

Adding 1 and 2

GM+ EM=1/2 AB+1/2 CD

EG=1/2(AB+CD)

HENCE PROVED.

HOPE THIS HELP YOU.