In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

ABCD is a rectangle and P,R and S are the mid - points of the AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

ABCD is a parallelogram, E is the mid-point of AB and CE bisects angleBCD . Then angleDEC is

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

ABCD a parallelogram, and A_1 and B_1 are the midpoints of sides BC and CD, respectively. If vec(A A)_1 + vec(AB)_1 = lamda vec(AC) , then lamda is equal to

Two adjacent sides of a parallelogram are 4.5 cm and 3 cm. Find its perimeter.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertex A and C on diagonal BD. Show that (i) DeltaAPB~=DeltaCQD (ii) AP=CQ .

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(EF) .