Question

if a triangle and parallelogram lie on the same base and between the same parallels then prove that the area of the triangle is equal to the half of the area of parallelogram

Answer 1

here is your answer ⭐⭐

Take a ABC and a ||gm BCDE on the same Base BC and between the same parallel lines BC and AD

We have to prove-: ar (ABC) = 1/2 ar (|| gm BCDE ).

CONSTRUCTION-: Draw AL perpendicular to BC ,meeting BC in L and DM perpendicular to BC meeting BC produced in M.

proof -: since BC || AD we have AL = DM.

ar ( ABC ) = 1/2 × BC ×AL = 1/2 × BC × DM [ AL = DM ]

=1/2 ×ar ( || gm BCDE ) (PROVED )