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D is any point on the side BC of triangle ABC. P and Q are centroids of triangle ABD and triangle ADOrespectively. Let us prove that PQ || BC. |
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Answer» -STEP explanation:In△ABC,D is the mid-point of AB and D is any point on BC. IfCQ∣∣PD meets AB in Q.ThenIn△ABC,we have to PROVE that BPQ= 21 ar(ABC)CONSTRUCT DC. Since D is the mid point of AB in △BC,CD is the median.ar(△BCD)= 21 ar(△ABC)−(i)Since △PDQ&△PDC are in the same PD and between the same PARALLEL lines PD&QC.∴ar(△PDQ)=ar(△PDC)−(II)From(i)&(ii)ar(△BCD)= 21 ar(△ABC)ar(△BPD)+ar(△PDQ)= 21 ar(△ABC){areaof△PDC=PDQ}⟹ar(△BPQ)= 21 ar(△ABC)Hope it is helpful to you |
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