Mathematics
Any point D is taken on the side BC of a ∆ABC and AD is produced to E such that AD = DE, prove that area of ∆BCE = area of ∆ABC.
Theorems on Area
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Answer
∆ABC with point D on the side BC and AD produced to E such that AD = DE is shown below:
In ∆ABE, it is given that AD = DE.
∴ BD is the median of ∆ABE
⇒ area of ∆ABD = area of ∆BED …….. (i)
Similarly,
In ∆ACE, it is given that AD = AE
∴ CD is the median of ∆ACE
⇒ area of ∆ACD = area of ∆CED …….. (ii)
By adding (i) and (ii), we get
⇒ area of ∆ABD + area of ∆ACD = area of ∆BED + area of ∆CED
⇒ area of ∆ABC = area of ∆BCE.
Hence, proved that area of ∆ABC = area of ∆BCE.
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