Page 55 - Mathematics Class - IX

OBSERVATIONS

1
Area ∆ABC = × × BC AE
2

1
Area ∆PQR = × × QR PD
2

 AE = PD (Perpendicular distance between two parallels)


Area of ∆ABC = Area of ∆PQR [ BC = QR]

INFERENCE

This verifies that

1. Area of parallelograms between same parallels and on the same base are equal.

2. Area of triangles on the same base and between same parallels are equal.

EXTENDED TASK

1. Verify that the area of a triangle is half the area of a parallelogram on the same base and between the same
parallels.
2. Construct a model of bridge using triangles and parallelograms.

APPLICATION

This result helps in solving various geometrical problems and to derive the formula for the area of a parallelogram
and a triangle.

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