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Question

Match the figures with appropriate results.
  1. ar∆ABE=ar∆ACE
  2. ar∆BED=1/4 ar∆ABC
  3. ar∆ABC=ar∆ADB


Solution

The correct option is
In Δ CNO and Δ DMO
CNO=DMO=900
CON=DOM [Vertically opposite angles]
OC = OD [Given]
ΔCNO=ΔDMO [AAS congruency]
CN=DM [CPCT]
Area ΔABC=12×AB×CN
Area  ΔABD=12×AB×DM
ar(ΔABC)=ar(ΔABD)

AD is the median for ΔABC [Given]
ar(ΔABD)=ar(ΔACD)
[Median of the triangle divides it into 2 triangles of equal area]
BE is the median ΔABD [Given]
ar(ΔBED)=ar(ΔABE)
ar(ΔBED)=12×ar(ΔABD)
ar(ΔBED)=12×12ar(ΔABC)
ar(ΔBED)=14ar(ΔABC)

AD is the median for ΔABC [Given]
ar(ΔABD)=ar(ΔACD)...(i)
[Median of the triangle divides it into 2 triangles of equal area]
ED is the median ΔEBC [Given]
ar(ΔBED)=ar(ΔCED)...(ii)
(i) - (ii)
 arΔABE=arΔACE

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