Question

ABCD is a quadrilateral in which AB=CD and AD =BC.Show that it is a parallelogram..​

Answer 1

Step-by-step explanation:

Here's your answer !!

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Given That :

In a quadrilateral ABCD -

AB = CD

AD = BC

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Construction :

Draw a diagonals AC and BD.

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Proof :

In ∆ ABC and ∆ ADC ,

AB = CD { given }

AD = BC { given }

AC = CA { common }

By S.S.S. criteria,

∆ABC is congruent to ∆ADC

\angle{\bf{ B }}∠B = \angle{\bf{D}}∠D { c.p.c.t. }

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In ∆ ABD and ∆ CDB ,

AB = CD { given }

AD = BC { given }

BD = DB { common }

By S.S.S. criteria,

∆ABD is congruent to ∆CDB

\angle{\bf{ A }}∠A = \angle{\bf{C}}∠C { c.p.c.t. }

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We know, of pair of opposite angles of a quadrilateral are equal, then it is a parallelogram.

Since ,

\angle{\bf{ B }}∠B = \angle{\bf{D}}∠D

\angle{\bf{ A }}∠A = \angle{\bf{C}}∠C

which are pairs of opposite angles of the quadrilateral.

Therefore,

ABCD is a parallelogram.

[ Hence Proved ]

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Thanks !!

Answer 2

ABCD is a parallelogram.

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