Question

AD is a one of the median of a AABC. X is any point on AD
show that
ar (ABX) = ar (AACX)
B​

Answer 1

Step-by-step explanation:

arABD=arACD(median divide in two parts of equal area).......(1)

arXBD=arXCD.......(2)

Subtract 2 from 1

arABD-arXBD=arACD-arXCD

arABX=arACX

Mark as brainliest if I deserve it

Answer 2

SOLUTION:

In △ABC, AD is the median and median divides a triangle into two triangles of equal area.

∴ ar(△ABD) = ar(△ACD) _____(i)

Again, in △XBC, XD is the median

∴ ar(△XBD) = ar(△XCD) _____(ii)

Subtracting (ii) from (i), we get

⇒ar(△ABD) - ar(△XBD) = ar(△ACD) - ar(△XCD)

⇒ar(△ABX) = ar(△ACX)