Question

two lines AB and CD bisect each other at O .prove that CA=BD

Answer 1

hello friend,
first, join AC,CB, BD and DA
now, consider triangle AOC and triangle BOD
                AO = BO (as AB and CD bisect each other)
                OC = OD (as AB and CD bisect each other)
      angleAOC= angleBOD (vertically opposite angles)

              so, triangleAOC is congruent to triangleBOD
                now, CA = BD (by c.p.c.t)

hence proved