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

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

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.

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)

In DeltaABC , E and F are the points on the sides AB and AC respectively. IF AE=2 cm, EB=2.5 cm, AF=4 cm, and FC=5 cm, then………………

ABCD is a parallelogram and P, Q are the mid points of bar(AD) and bar(BC) respectively. Show that : bar(BD) and bar(PQ) bisect each other.

In a parallelogram ABCD, P is the mid point of the side AD. The line BP cuts the diagonal AC in the point Q. Then the ratio AQ:QC=

In DeltaABC , if D, E, F are the midpoints of the sides BC, CA and AB respectively, then what is the magnitude of the vector bar(AD)+bar(BE)+bar(CF) ?

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

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

Draw a triangle ABC and mark the midpoints E and F of two sides of triangle. bar(AB) and bar(AC) respectively. Join the point E and F as shown in the figure. Measure EF and the third side BC of the triangle. Also measure angleAEF and angleABC . We find angleAEF = angleABC and bar(EF)=(1)/(2)bar(BC) As these are corresponding angles made by the transversal AB with lines EF and BC, we say EF"||"BC.