Answer :

Let us drop a perpendicular AG and BH to CD cutting EG at I and J and CD.

In ΔADG & ΔAEI,

∠AGD = ∠AIE |Right Angle

∠AEI = ∠ADG |corr. ∠s

ΔADG~ΔAEI by AA Similarity Rule

In ΔBJF & ΔBHC,

∠BJF = ∠BHC |Right angle

∠BFJ = ∠BCH |corr. ∠s

ΔBJF~ΔBHC by AA Similarity Rule

In rectangle ABHG & ABJI,

AI = BJ …(a) |opposite sides of rectangle are equal

AG = BH …(b) |opp. sides of rectangle

From eqn. (b) – (a)

AG – AI = BH – BJ

⇒ GI = HJ

…(2)

From (1) & (2),

Hence, proved.

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