Question

ABCD IS quadrantal in which AB equal to CD and AD equal to BC show that it is a parallelogram in one of the diagonal

Answer 1

Answer:

given ,

AB = CD

AD = BC

to prove that : ABCD is a IIgram

proof :- AB = CD (from the given )

BC = AD (from the given )

BD = BD (common side )

∴ Δ ADB ≡ Δ DBC by SSS congruence rule .

therefore from CPCT we can write that ∠ADB

= ∠ DBC (alternate interior angle )

since the alternate interior angles and opposite sides are equal in a quadrilateral therefore it is a IIgram .

i hope it helps ....................^_^