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Solv this theoram cls 9 Ka h okh |
| Answer» ABC and △ABD are two trianles on same base AB such that area(△ABC)=area(△ABD).JOIN CDTo prove:CD∥ABConstruction:DRAW the altitutdes of △ABC and △ABD THROUGHT C and D and MEETING base at E and F respectively.Proof:Since CE⊥AB and DF⊥AB(by construction)Since, lines perpendicular to same line are parallel to each other.∴CE∥DF .(1)Now, area(△ABC)= 21 ×AB×CEarea(△ABD)= 21 ×AB×DFSince area(△ABC)=area(△ABD)(Given)∴CF=DF ... (2)Now, In CDFE,CF∥DF and CE∥DFSince one pair of opposite sides are equal and parallelHence CDFE is a parallelogram.So, CD∥EF (opposite sides of parallelogram are parallel)∴CD∥AB | |