Show that the Diagonals of a Parallelogram Divide It into Four Triangles of Equal Area. - Mathematics

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Show that the diagonals of a parallelogram divide it into four triangles of equal area.

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Solution

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.

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Chapter 9: Areas of Parallelograms and Triangles - Exercise 9.3 [Page 162]

APPEARS IN

NCERT Mathematics Class 9
Chapter 9 Areas of Parallelograms and Triangles
Exercise 9.3 | Q 3 | Page 162

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