Prove that in a paralleogram, the lines joining a pairof opposite vert

1.	Prove that in a paralleogram, the lines joining a pairof opposite vertices to the mid-points of a pair ofopposite sides trisect a diagonal.
Answer» 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)

Prove that in a paralleogram, the lines joining a pairof opposite vertices to the mid-points of a pair ofopposite sides trisect a diagonal.

Answer»

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)