Question

Prove that in a parallelogram,the lines joining a pair of opposite vertices to the midpoints of a pair of opposite side trisect a diagonal

Answer 1

hey mate!

In ||gm ABCD, E is the mid-point of AB and F is the mid-point of DC. Also AB|| DC.

AB = DC and AB || DC

∴ (1/2)AB = (1/2)DC and AE || DF (Since E and F mid point of AB and DC)

∴ AE = (1/2)AB and DF = (1/2)DC

∴ AE = DF and AE || DF

∴Quadrilateral AEFD is a parallelogram Similarly, Quadrilateral EBCF is a parallelogram.

Now parallelogram AEFD and EBCF are on equal bases DF = FC and between two parallels AB and DC

∴ ar(||gm AEFD) = ar(||gm EBCF)

Answer 2

Answer:

Hey mate plzz refer to the attachment