9303753286127016 In the given figure AB||PQ||CD, AB = x units, CD= y units and PQ = z units, then 1/x + 1/y=_______

In the given figure AB||PQ||CD, AB = x units, CD= y units and PQ = z units, then 1/x + 1/y=_______

In Δ FDC and Δ FBA,

∠FDC = ∠FBA [As DC || AB]

∠DFC = ∠BFA [common angle]

Hence, ∆FDC ~ ∆FBA by AA criterion for similarity.

So, we have DC/AB = DF/BF z/x = DF/BF …. (1)

In Δ BDC and Δ BFE, ∠BDC = ∠BFE [As DC || FE]

∠DBC = ∠FBE [Common angle]

Hence, ∆BDC ~ ∆BFE by AA criterion for similarity.

So, we have BD/BF = z/y ….. (2)

Now, adding (1) and (2), we get

BD/BF + DF/BF = z/y + z/x

1 = z/y + z/x

Thus, 1/z = 1/x + 1/y

Answer

1/x + 1/y = 1/z 

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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