ABCD is a parallelogram and AP and CQ are perpendicular from vertices A and C on diagonal BD. Show that
`DeltaAPB approx DeltaCQD`

AP=CQ

ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that (i) DeltaAPB ~= DeltaCQD (ii) AP = CQ

In parallelogram ABCD two points P and Q are taken on diagonal BD such that DP=BQ show that DeltaAPD approx Delta CQB DeltaAQB approx Delta CPD AQ=CP APCQ is a parallelogram

ABCD is a parallelogram, with AC, BD as diagonals. Then vec AC - vec BD =

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

In DeltaABC and DeltaDEF, AB=DE,AB||DE, BC=EF and BC||EF Vertices A,B and C are joined to vertices D , E and F respectively show that quadrilateral ABED is a parallelogram quadrilateral BEFC is a parallelogram AD||CF and AD=CF quadrilateral ACFD is a parallelogram AC=DF DeltaABC approx DeltaDEF .

ABCD is a quadrilateral in which P, Q, R and S are mid- points of the sides AB, BC, CD and DA. AC is a diagonal. Show that : PQRS is a parallelogram.

ABCD is a quadrilateral in which P,Q,R and S are mid points of the sides AB,BC,CD and DA. AC is a diagonal Show that: SR||AC and SR=1/2 AC PQ=SR PQRS is a parallelogram

In a parallelogram ABCD, E and F are the mid points of sides AB and CD respectively (see fig.) Show that the line segements AF and EC trisect the diagonal BD.

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

In the following figure, ABCD is parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect AD = CQ. If AQ intersect DC at P, Show that ar (BPC) = ar (DPQ)