In figure- two lines AB and CD intersect each other the point O such that BCparallel DA- Show that O is the mid-point of both the line-segments AB and CD-

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In-x394-COB-amp-x394-AOD-verticallyoppositeange-x2220-COB-x2220-AOD-alternateinteriorangle-AB-BC-given-x2234-x394-COB-x2245-x394-AOD-ASAcongurency-x2234-OB-OA-CPCT-andOC-OD-CPCT-andhenceOisthemidpoint-

In figure, two lines AB and CD intersect each other at the point O such that BC∥DA. Show that O is the mid-point of both the line-segments AB and CD.

InΔCOB&ΔAOD(verticallyoppositeange)∠COB=∠AOD(alternateinteriorangle)AB:BC(given)∴ΔCOB≅ΔAOD(ASAcongurency)∴OB:OA(CPCT)andOC=OD(CPCT)andhenceOisthemidpoint.

In figure, two lines $A B$ and $C D$ intersect each other at the point $O$ such that $B C ∥ D A$ . Show that $O$ is the mid-point of both the line-segments $A B$ and $C D$ .