1. E is any point on median AD of a triangle ABC. Show that area of triangle ABE = area of triangle ACE.

Dear Student,

Since, AD is the median of ΔABC, it will divide ΔABC into two triangles of equal areas.

∴ Area (ΔABD) = Area (ΔACD) ... (1)

Now, ED is the median of ΔEBC.

∴ Area (ΔEBD) = Area (ΔECD) ... (2)

From (1) and (2):

Area (ΔABD) − Area (EBD) = Area (ΔACD) − Area (ΔECD)

Therefore, Area (ΔABE) = Area (ΔACE)

 

We hope that clarifies your query.

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