P,Q,R are the points on the sides AB, BC and CA respectivelyh of `/_\ABC such that `AP:PB=BQ:Qc=AR:RC=1:2`. Show that POBQR is a parallelogram

P,Q,R are the points on the sides AB, BC and CA respectively of triangle ABC such that AP:PB=BQ:QC=AR:RC=1:2. Show that PBQR is a parallelogram.

P,Q,R and S are the mid-poins of the sides AB,BC,CD and DA respectively of quad. ABCD. Show that PQRS is a parallelogram such that ar(||gmPQRS) = 1/2 ar(quad.ABCD)

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PB = QC

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PQ = QR

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

ABCD is a square. P, Q, R, S are points on the sides AB. BC, CD, DA respectively such that AP = BQ = CR = DS. What is angleSPQ equal to ?

Let P, Q, R, S be respectively the midpoints of the sides AB, BC, CD and DA of quad. ABCD Show that PQRS is a parallelogram such that ar("||gm PQRS")=(1)/(2)ar("quad. ABCD") .

P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of ||gm ABCD. Show that PQRS is a parallelogram and also show that ar("|| gm PQRS")=(1)/(2)xxar("||gm ABCD) .

P and Q are points on the sides AB and AC respectively of a triangleABC . If AP= 2cm, PB = 4cm AQ= 3cm and QC= 6cm. Show that BC= 3PQ.