In the figure, ABC and ABD are two triangles on the base AB. If line segment CD is bisected by AB at O, show that ar (△ABC)=ar(△ABD)
Given : in the figure, △ABC and △ABD are on he same base AB and line CD is bisected by AB at O. Hence, CO = OD.
To prove : ar(△ABC)=ar(△ABD)
Construction : Draw CL⊥ABandDM⊥AB
Proof : In △CLOand△EMO∠L=∠MCO=OD∠COL=∠DOM∴△CLO≅△DMO
∴CL=DM (By CPCT)
Now ar (△ABC)=12Base×Height=12×AB×CLand ar (△ADB)=12×AB×DM=12AB×CL