Question

show that PREF is a parallelogram

Answer 1

given pqrs is a llgm therefore PQ = RS

to prove : PERF is a llgm

proof :
in llgm PQ = RS (opp sides of llgm are equal)
therefore 1/3 PQ = 1/3 SR

NOW EQ equals 2 PE
and EQ + PE = PQ
therefore PE + PE + PE = PQ
therfore PE = 1/ 3 PQ

similarly FR = 1/3 SR

NOW in PERF, PE= FR & FR ll PE
therfore PERF is a llgm

hence proved
now PE = 1/3 PQ
height × PE = 1/3 height × PQ
area PERF = 1/3 PQRS
HENCE PROVED