1.

The median of triangle ABC intersect at G show that area of triangle BGC is half or triangle ABC​

Answer»

Step-by-step EXPLANATION:

CONSIDER the a above figure

given, BG is the MEDIAN of ∆ABC

we draw BM।।CA

so,

ca = 2cg

here, BM is the height of ∆ABC and ∆BCG

now,

area \: of \: abc = \frac{1}{2} \times ca \times bm \\ area \: of \: bcg = \frac{1}{2} \times cg \times bm

now, comparing their areas,

\frac{abc}{bcg} = \frac{ \frac{1}{2} \times ca \times bm }{ \frac{1}{2} \times cg \times bm} = \frac{ca}{cg} = \frac{2cg}{cg } =2 \\ > \frac{abc}{bcg} = 2 \\ > abc = 2bcg

hence, proved


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