Mathematics
In the given figure, AP is parallel to BC, BP is parallel to CQ. Prove that the areas of triangles ABC and BQP are equal.
Theorems on Area
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Answer
We know that,
Triangles on the same base and between the same parallel lines are equal in area.
Since, triangle ABC and BPC lie on the same base BC and between the same parallel lines AP and BC.
∴ Area of △ ABC = Area of △ BPC ………(1)
Since, triangle BPC and BQP lie on the same base BP and between the same parallel lines BP and CQ.
∴ Area of △ BPC = Area of △ BQP ………(2)
From equations (1) and (2), we get :
Area of △ ABC = Area of △ BQP.
Hence, proved that area of △ ABC = area of △ BQP.
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