Q. 115.0( 5 Votes )

# ABCD is a trapezium in which AB || CD and AD = BC, then ∠A = ∠B is

A. true

B. false

Answer :

Construction: Draw perpendicular line from D and C to AB such that it cuts AB at F and E, respectively.

Now, In ∆ADF and ∆BCE,

AD = BC (Given)

∠AFD = ∠BEC (90^{o} each)

DF = CE (Perpendicular distance between the same parallels)

∴ By SSA axiom

∆ADF ≅ ∆BCE

∠A = ∠B (by c.p.c.t.)

Therefore Option A is correct.

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