Prove the the opposite angles of a parallelogram are equal.

Explanation

GIVEN `A||gm` ABCD in which `AB||DC` and `AD||BC`.
TO PROVE `angleA=angleC and angleB=angleD`.
PROOF `AB||DC` abd AD is a transversal,
`:. angleBAD+angleADC=180^(@)` ....(i)
Again, `AD||BC` and DC is a transerversal.
`:. angleADC+angleDCB=180^(@)`. ...(ii)
From (i) and (ii), we get
`angleBAD+angleADC=angleADC+angleDCB`
`implies angleBAD=angleDCB implies angleA=angleC`.
Similarly, `angleB=angleD`.
Hence, `angleA=angleC and angleB=angleD`.