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 and AP and CQ are perpendicular from vertices A and C on diagonal BD. Show that DeltaAPB approx DeltaCQD AP=CQ

In parallelogram ABCD , P is a point on BC. In Delta DCP and Delta BLP , DP : PL is equal to :

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.

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).

The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where ‘P’ is any point on side AB. Prove that CQ xx PQ = QA xx QD .

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.

Let A be one point of intersection of two intersecting circles with centres O and Qd . The tangents at A to the two circles meet the circles again at B and C respectively. Let the point P be located so that AOPQ is a parallelogram. Prove that P is the circumcentre of the triangle ABC.

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed . Show that ar (ABCD) = ar (PBQR)

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