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CBSE Class 9 Answered

In triangle ABC, D is the mid point of AB. P is any point on BC. CQ PD meets AB at Q. Show that ar (BPQ) =  ar (ABC).
Asked by Topperlearning User | 13 Dec, 2013, 01:36: AM
answered-by-expert Expert Answer
Given: ABC in which D is the mid point of AB.PD CQ
Construction: Join C to D and Q to P.
Proof: CD is a median of the ABC    
 ar (BCD) = ar (DAC)
PDC and PDQ are on the same base PD and between the same parallels PD and CQ.
 ar (PDC) = ar (PDQ)
ar (BCD) =  ar (ABC)          (median divides a triangle into two triangles of equal area) 
ar (BPD) + ar (PDC) =   ar (ABC)
ar (BPD) + ar (PDQ) =   ar (ABC)
Hence ar (BPQ) =  ar (ABC)                                   ( BPD + PDQ =  BPQ)
Answered by | 13 Dec, 2013, 03:36: AM

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