Question

two triangles having the same base and equal area lie between the same parallels

Answer 1

$\underline{\huge\textbf{Solution :}}$


GIVEN : Two triangles ∆ABC and ∆ABD have the same base AB and ar(∆ABC) = ar(∆ADB).


TO PROVE : CD || AB.


CONSTRUCTION : Draw CP perpendicular to AB and DQ perpendicular to AB.


PROOF : Since CP perpendicular to AB and DQ perpendicular to AB , we have -


CP || DQ ( Since , lines perpendicular to same line are parallel ).


Now , ar(∆ABC) = ar(∆ABD)

➨ 1/2 × AB × CP = 1/2 × AB × DQ


( Since , Area of a ∆ = 1/2 × b × h )

➨ CP = DQ


Now , CP || DQ , & CP = DQ


➨ CPDQ is a parallelogram.


➨ CD || PQ ➨ CD || AB.


Thus , the two triangles lie between the same parallels.



$\boxed{\huge{Hence \:Proved\:!}}$