If the median of a △ABC intersect at G. show that ar (△AGC) = ar (△AGB) = ar (△BGC) = 1/3 ​ ar (△ABC)

If the medians of a triangle A B C intersect at G , show that a r( triangle A G B)=a r(triangle A G C)=a r(triangle B G C)=1/3a r( triangle A B C) . GIVEN : triangle A B C such that its medians A D ,B E and C F intersect at G TO PROVE : a r(triangle A G B)=a r(triangle B G C)=a r(triangle C G A)=1/3 ar (triangle A B C) .

In fig, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that: (i) ar(BDE)= 1/4 ​ ar(ABC) (ii) ar(BDE)= 1/2 ​ ar(BAE)

The medians of Delta ABC intersect at point G. Prove that: area of Delta AGB = (1)/(3) xx " area of " Delta ABC

AD, BE and CF asre the medians of a triangle ASBC intersectiing in G. Show that /_\AGB=/_\BGC=/_\CGA=1/3/_\ABC .

Use the informations given in the following figure to show that ar. (ABCQ) = ar (ABCDE) [Given : l // m and p//n ]

In the given figure, AP ||BQ ||CR . Prove that ar(Delta AQC) = ar (DeltaPBR)

Given a parallelogram ABCD where X and Y are the mid-points of the sides BC and CD respectively . Prove that: ar (Delta AXY) = (3)/(8) xx ar (//gm) ABCD

In DeltaABC , if L and M are the points on AB and AC, respectively such that LM || BC . Prove that ar (DeltaLOB) = ar (DeltaMOC) .

In figure, CD || AE and CY || BA . Prove that ar (DeltaCBX) = ar (DeltaAXY) .

If the points A (x,y),(-1,3)and(5,-3) ar collinear, then show that x + y = 2.