Mathematics
In the given figure, a point D is taken on side BC of ΔABC and AD is produced to E, making DE = AD. Show that :
ar (ΔBEC) = ar (ΔABC).
Theorems on Area
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Answer
Since, AD = DE thus, D is the mid-point of AE.
Median BD divides ΔABE into two Δs of equal area.
ar (ΔABD) = ar (ΔEBD) ….(1)
Median CD divides ΔACE into two Δs of equal area.
ar (ΔACD) = ar (ΔECD) ….(2)
Adding the Equations:
ar (ΔABD) + ar (ΔACD) = ar (ΔEBD) + ar (ΔECD)
∴ ar (ΔABC) = ar (ΔBEC)
Hence, proved that ar (ΔBEC) = ar (ΔABC).
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Related Questions
In the given figure, D is the mid-point of BC and E is any point on AD. Prove that :
(i) ar (△EBD) = ar (△EDC)
(ii) ar (△ABE) = ar (△ACE)
In the given figure, D is the mid-point of BC and E is the mid-point of AD. Prove that :
ar (ΔABE) = ar (ΔABC).
If the medians of a ΔABC intersect at G, show that :
ar (ΔAGB) = ar (ΔAGC) = ar (ΔBGC) = ar (ΔABC).
D is a point on base BC of a ΔABC such that 2BD = DC. Prove that :
ar (ΔABD) = ar (ΔABC).
