Diagonal PR divides parallelogram PQRS into equal triangles PSR and PQR. Similarly, triangles OSR and OQR share base and equal heights, making their areas equal. Subtracting gives area(ΔPSO) = area(ΔPQO).
O is any point on the diagonal PR of a parallelogram PQRS. Prove that the areas of triangles PSO and PQO are equal.
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Diagonal PR divides parallelogram PQRS into two triangles of equal area:
Area(ΔPSR) = Area(ΔPQR) … (Equation 1).
Draw perpendiculars from vertices S and Q to diagonal PR. Since PQRS is a parallelogram, these two altitudes are equal.
Triangles OSR and OQR share base OR and have equal altitudes from S and Q:
Area(ΔOSR) = Area(ΔOQR) … (Equation 2).
Subtracting Equation 2 from Equation 1:
Area(ΔPSR) – Area(ΔOSR) = Area(ΔPQR) – Area(ΔOQR)
Area(ΔPSO) = Area(ΔPQO).
Hence proved.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
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