Question

In figure,AN andCP are Perpendicular to the diagnoal BD of a parallelogram ABCD. Prove that:
1.ΔADN congruent ΔCBP
2.AN=CP.

Answer 1

given
ABCD is a parallelogram where AN and CP are perpendicular to the diagonal BD
to prove
ΔADN congruent ΔCBP
AN=CP
proof
in between ΔADN and ΔCBP
AD=BC
angleCPB=angleAND
PBC=ADN
so
ΔADN congruent ΔCBP(aas cong.)
hence by cpct
AN=CP
proved