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CBSE Class 9 Answered

Prove that the triangles between the same parallels and on the same base are equal in area.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer
ABC and PBC are on the same base BC and between the same parallels BC and AP.
To Prove: ar (ABC) = ar (PBC)
Construction; Through B, draw BD  CA intersecting PA produced at D, and Through C draw CQ  BP intersecting BP produced at Q.
Proof: BCQP is a parallelogram with diagonal PC.
ar (BCP) = ar (BCQP)
Again BCAD is also a parallelogram with diagonal AB
ar (ABC) = ar (ADBC)
Since parallelogram BCQP and parallelogram BCAD are on the same base BC and between the same parallels BC and DQ;
 ar (BCQP) = ar (BCAD)
ar (BCQP) = ar (BCAD)
 ar (BCP) = ar (ABC)
Hence ar (ABC) = ar (BCP)
Answered by | 04 Jun, 2014, 03:23: PM

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