Question

ABC
a quadrilateral in which AB=CD and AD=BC. Show that it is a parallelogram
. [Hint: Draw one of the diagonal]​

Answer 1

Step-by-step explanation:

answer is in picture.

Hope it helps.

Answer 2

$\huge{\mathfrak{\bigstar{\underline{\underline{\red{Solution:-}}}}}}$

$\sf{Draw\: diagonal\: BD.}$

$\sf{In \:angle\:ABD\: and \:angle\:CDB,}$

$\sf{AD || CB}$

$\sf{Therefore\: angle\:1 = angle\:2}$

$\sf{Also,\: BD = DB}$

$\sf{Therefore\: angle\: ABD = angle\: CDB}$

$\sf{=> angle\:3 = angle\:4}$

$\sf{Therefore\: AB||CD}$

$\sf{So\: both\:pairs\: of\: opposite \:sides \:are\: parallel.}$

$\sf{Thus\:ABCD\: is \:a \: parallelogram}$