Question

line segment AB is Parallel to another equal line segment CD. O is the mid point of ad. prove that​

Answer 1

$Given: AB \: is \: parallel \: to \: another \\ \: line \: segment \: CD. </p><p></p><p>            \\ O \: is \: the \: midpoint \: OF \: AD</p><p></p><p>$

$In ΔAOB and ΔDOC \\ \\ </p><p></p><p>∠AOB=∠COD         ...(Vertically \: opposite \: angle ) \\ \\ </p><p></p><p> \\ ∠BAO=∠CDO         ...(Given \: AB \: parallel  \: to </p><p></p><p>$

$DC \: and \: AD \: \\ meet  \: both \: lines \: \\ so alternate angles \: are equal)$

$AO=OD          ....(O \: is \: the \: midpoint \: of \: AD )</p><p></p><p>ΔAOB≅ΔDOC        ...ASA \: test \\ </p><p></p><p>So, BO=CO \\ </p><p></p><p>Then, O \: is \: the \: midpoint \: of \: BC.</p><p></p><p>$