Question

13. Line segment joining the vertices of two triangles is
bisected by their common base, on the opposite sides of
which these vertices lie. Prove that the two triangles are
equal in area.​

Answer 1

Answer:

Line segment joining the vertices of two triangles is AD.

AD is bisected by the common base BC

∴ AM = MD

Now

Ar ( triangle ABC)= (1/2) BC* AM ...... (1)

Ar ( triangle BCD)=(1/2) BC* DM ...... (2)

since AM = DM

Therefore (1) = (2)

Hence Ar ( triangle ABC)=Ar ( triangle BCD)

proved.