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# In Fig. 9.30, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC).

Q : 2        In Fig. $\small 9.30$, D and E are two points on BC such that  $\small BD=DE=EC$. Show that  $\small ar(ABD)=ar(ADE)=ar(AEC)$.

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In $\Delta$ABC, D and E are two points on BC such that BD = DE = EC

AD is the median of ABE, therefore,

area of ABD= area of AED...................(1)

AE is the median of ACD, therefore,

area of AEC= area of AED...................(2)

From (1) and (2)

area of ABD=area of AED= area of AEC
Hence proved

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