Question

Prove that in a paralleogram, the lines joining a pair
of opposite vertices to the mid-points of a pair of
opposite sides trisect a diagonal. (Fig. 9.25)​

Answer 1

Answer:

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Step-by-step explanation:

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)