Question

help me in these questions

Answer 1

2️⃣
AD is the median of ΔABC.

Therefore, it will divide ΔABC into two triangles of equal area.

∴ Area (ΔABD) = Area (ΔACD)

=> Area (ΔABD ) = (½) area (Δ ABC) ------(1)

In ΔABD, E is the mid-point of AD.

Therefore,

BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

Area (ΔBED) = (1/2)Area (ΔABD)

Area (ΔBED) = (1/2) x(1/2) Area (ΔABC)         [From (1)]

∴ Area (ΔBED) = (1/4)Area (ΔABC)

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3️⃣
We know that diagonals of parallelogram bisect each other.

Therefore, O is the mid-point of AC and BD.

BO is the median in ΔABC. Therefore, it will divide it into two triangles of equal areas.

Area (ΔAOB) = Area (ΔBOC) ... (1)

In ΔBCD, CO is the median.

Area (ΔBOC) = Area (ΔCOD) ... (2)

Similarly, Area (ΔCOD) = Area (ΔAOD) ... (3)

From equations (1), (2), and (3), we obtain

Area (ΔAOB) = Area (ΔBOC) = Area (ΔCOD) = Area (ΔAOD)

Therefore, it is evident that the diagonals of a parallelogram divide it into four triangles of equal area.