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In Fig.9.28, A P\ ||\ B Q\ ||\ C R. Prov...

In Fig.9.28, `A P\ ||\ B Q\ ||\ C R`. Prove that `a r\ (A Q C)\ =\ a r\ (P B R)dot`

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Since `triangleABQ` and `trianglePBQ` lie on the same base `BQ` and are between the same parallels `AP` and `BQ`,
According to Theorem 9.2: Two triangles on the same base (or equal bases) and between the same parallels are equal in area.
`Area (triangleABQ) = Area (trianglePBQ)` ...(1)
Similarly, `triangleBCQ` and `triangleBRQ` lie on the same base `BQ` and are between the same parallels `BQ` and `CR`.
`Area (triangleBCQ) = Area (triangleBRQ`) ... (2)
On adding Equations (1) and (2), we obtain
`Area (triangleABQ) + Area (triangleBCQ) = Area (trianglePBQ) + Area (triangleBRQ)`
Hence, `Area (triangleAQC) = Area (trianglePBR)` is proved.
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