Math, asked by piyushkumar246890, 4 months ago

lf one pair of opposite side are equal and parallel of any quadrilateral. proof that this must be parallelogram​

Answers

Answered by Sriramgangster
17

Answer:

\textbf{Hope it helps.}

\textbf{Mark me as}  \bold{\boxed{Brainliest}}

Step-by-step explanation:

Given: ABCD is quadrilateral and AB║CD, AB=CD.

To prove: ABCD is a parallelogram

Proof: AC is a transversal and also AB║CD, therefore

∠BAC=∠DCA(Alternate angles)

In ΔADC and ΔCBA, we have

AB=CD(Given)

∠BAC=∠DCA(Alternate angles)

AC=CA(Common)

ΔADC≅ΔCBA by the SAS rule.

Hence, by CPCT, DA=BC

Thus, Both the pair of opposite sides are equal in the quadrilateral ABCD, therefore ABCD is a parallelogram.

Hence proved.

Similar questions