Question

In a parallelogram ABCD, E and F are the midpoints of the sides AB and CD respectively. The line segments AF and BF meet the line segments DE and CE at points G and H respectively Prove that: ΔHEB ≅ ΔHFC

Answer 1

Since ABCD is a parallelogram,
AB = CD and AD = BC
Now, E and F are the mid-points of AB and CD respectively,
⇒ AE = EB = DF = FC ....(i)

In ΔHEB and ΔHFC,
BE = FC              ....[From (i)]
∠EHB = ∠FHC  ....(vertically opposite angles)
∠HBE = ∠HFC  ....(Alternate interior angles)
∴ ΔHEB ≅ ΔHFC.