Question

E is any point on median AD of a ABCD,Shown that area of ABE =Area of ACE.

Answer 1

Given : AD is a median of ABC and E is any point on AD.

To prove : ar (ABE) = ar (ACE)

Proof :   AD is the median of ABC

 ar (ABD) = ar (ACD) ...(1)            

also, ED is the median of EBC,

 ar (BED) = ar (CED) ...(2)

Subtracting (2) from (1), we get

ar (ABD) – ar (BED) = ar (ACD) – ar (CED)

 ar (ABE) = ar (ACE).