Question

1. Fig.9.23, E is any point on median AD of a
ABC. Show that ar (ABE) = ar (ACE).
)​

Answer 1

Given :- AD is a median of ABC.

To Prove :- ar.(ABE) = ar.(ACE)

Proof :-

In ABC,

AD is the median.

So, ar.(ABD) = ar.(ACD) -- (Equation 1)

In BEC,

ED is the median.

So, ar.(BED) = ar.(CED) -- (Equation 2)

Now, Equation 1 – Equation 2.

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

➣ ar.(ABE) = ar.(ACE)

Hence, Proved.

Answer 2

: Solution

Given,

➝ AD is median of ΔABC it will divide ΔABC into two triangles of equal area.

➝ ar(ABD) = ar(ACD) — (i)

also,

➢ ED is the median of ΔABC.

ar(EBD) = ar(ECD) — (ii)

➝ Subtracting (ii) from (i),

➢ ar(ABD) – ar(EBD) = ar(ACD) – ar(ECD)

➢ ar(ABE) = ar(ACE).

hence proved