E is the mid-point of side AB and F is the mid point of side DC of parallelogram ABCD . Prove that AEFD is a parallelogram.

X and Y are the mid-points of the opposite sides AB and DC of a parallelogram ABCD. Prove that squareAXCY is a parallelogram.

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.

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

In figure, P is the mid-point of side BC of a parallelogram ABCD such that angleBAP=angleDAP . Prove that AD = 2CD.

In triangle ABC, angle B is obtuse. D and E are mid-points of sides AB and BC respectively and F is a point on side AC such that EF is parallel to AB. Show that BEFD is a parallelogram.

L and M are the mid-points of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.

In triangle ABC, D and E are mid-points of sides AB and BC respectively. Also, F is a point in side AC so that DF is parallel to BC (i) Prove that DBEF is a parallelogram.

ABCD is a parallelogram. E is a point on BA such that BE =2 EA and F is a point on DC such that DF=2 FC. Prove that AECF is a parallelogram whose area is one third area of parallelogram ABCD.

E , F , G , H are respectively, the mid-points of the sides of parallelogram A B C D . Show that the area of EFGH is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join H and F

In Delta ABC , E is mid-point of side AB and EBCD is a parallelogram. If the area of Delta ABC is 80 cm, find the area of parallelogram EBCD.