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Proof- AB = DC [Sides of parallelogram] .........................(1)
In triangles. DCE and FBE
∠E = ∠E [Vertically opp. ∠s]
and, ∠D = ∠F [Alt. Int ∠s]
so, Triangle DCE & FBE are Similar By AA Criteria
hence, DC/FB = CE/BE = DE/FE
But CE/BE = 1 [∵E is the mid point]
so, 1 = DC/FB
so, DC =FB
so By Eqn (1)
AB= FB
so, AF = AB+FB
AF = 2AB [∵AB=FB]
In triangles. DCE and FBE
∠E = ∠E [Vertically opp. ∠s]
and, ∠D = ∠F [Alt. Int ∠s]
so, Triangle DCE & FBE are Similar By AA Criteria
hence, DC/FB = CE/BE = DE/FE
But CE/BE = 1 [∵E is the mid point]
so, 1 = DC/FB
so, DC =FB
so By Eqn (1)
AB= FB
so, AF = AB+FB
AF = 2AB [∵AB=FB]
triangle15:
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