Question

prove that bisectors of opposite angles of a parallelogram are parallel.

Answer 1

ABCD is parallelogram..............given 
DE bisect < D, BF bisect < B..................given 
<D = <B....................opposite angles of parallelogram are equal 
<1 = <2 ................equal angle bisect still equal 
<A = <C ....................opposite angles of parallelogram are equal 
AD = BC ......................opposite sides of parallelogram are equal 
ΔADE ≅ ΔCBF...................ASA 
DE = BF..................CPCTC

Answer 2

ABCD is parallelogram   (given )
DE bisect < D, BF bisect < B  (given )
<D = <B             (opposite angles of parallelogram are equal )
<1 = <2               (equal angle bisect still equal) 
<A = <C              .(opposite angles of parallelogram are equal )
AD = BC           (opposite sides of parallelogram are equal) 
ΔADE ≅ ΔCBF    by .ASA  congruence condition
DE = BF          BY.CPCT  PROVED