ABCD is a parallelogram. E is any point on the side BC, line segment drawn through D and E cards the extended AB at T Prove that `DE * EB = CE * TE`.

ABCD is a parallelogram. E is the middle point of the side CD. BE intersects AC at the point X. prove that AX=2/3AC .

E is any point on the side BC of the parallelogram ABCD. AE intersects the diagonal BD at point F. Prove that DF×EF=FB×FA .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.Prove that, AE^2+BD^2=AB^2+DE^2 .

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced at E.Prove that(ii) EL = 2BL

ABC is equilateral triangle and D,E are middle points of sides AB and AC then length of DE is

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that triangleABE~triangleCFB .

Two triangles ABC and DBC are in the same side of the common base BC. Lines drawn parallel to BA and BD from any point E on BC intersect AC and DC at the points P and Q respectively. Show that PQ is parallel to AD.

Line segment drawn parallel to the base BC of ∆ABC cuts AB and AC at D and E respectively. DP , AL and EQ are perpendicular on BC. Prove that LP : PB = LQ : QC .

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced Prove that (i) ALxxLM=CLxxBL

E is the mid point of the side AB of the square ABCD, if /_AED = theta then find the value of cos theta and sin theta .