Prove that a median divides a triangle into two triangles of equal area.

If A(4,-6),B(3,-2)and C(5,2) are the vertices of a DeltaABC and AD is its median, prove that the median AD divides DeltaABC into two triangles of equal areas.

Show that a median of a triangle divides it into two triangles of equal area.

Show that a median of a triangle divides it into two triangles of equal area. GIVEN : A triangle A B C in which A D is the median. TO PROVE : a r(triangle A B D)=a r( triangle A D C) CONSTRUCTION : Draw A L_|_B C

Show that a median of a triangle divides it into two triangles of equal areas.

You have studied in Class IX, (Chapter 9. Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ ABC whose vertices A(4, – 6), B(3, –2) and C(5, 2).

If A (1,2) , B(-2, 3) and C(-3,-4) be the vertices of DeltaABC . Verify that median BE divides it into two triangles of equal areas.

If A(4,-6),B(3,-2) a n d C(5,2) are the vertices of A B C, and AD is median then verify the fact that a median of a triangle ABC divides it into two triangles of equal areas.

There is an equilateral triangle with side 4 and a circle with the centre on one of the vertex of that triangle. The arc of that circle divides the triangle into two parts of equal area. How long is the radius of the circle?

Show that : (i) a diagonal divides a parallelogram into two triangles of equal area. (ii) the ratio of the areas of two triangles of the same height is equal to the ratio of their bases. (iii) the ratio of the areas of two triangles on the same base is equal to the ratio of their heights.

In Figure the line segment XY is parallel to side AC of DeltaA B C and it divides the triangle into two parts of equal areas. Find the ratio (A X)/(A B) .