Question

3. Prove that the line-segment joining the mid-points of two non-parallel sides of
a trapezium is parallel to the parallel sides.​

Answer 1

Step-by-step explanation:

construct as shown in figure

∆AEI congruent to ∆DEH

as AE= DE(since E is midpoint)

<HED = < IEA(vertically opposite)

<EHD=<EIA( AI || DH and HI transversal so alternate interior angles are equal)

therefore we get IE=HE => E is also midpoint of HI

extend EF to IC and let it intersect at point X.

Now X will be midpoint of IC

by midpoint theorem in ∆IHC we get EX ||HC.

Since F is a point on EX then EF || AC