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Prove that the median of Delta ABC divid...

Prove that the median of `Delta` ABC divides it into two triangles of equal area. .

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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 Delta ABC whose vertices are A(4, -6), B(3, -2) and C(5, 2).

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Prove that “the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides”.

Prove that the ratio at the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Prove that " the ratio of areas of two similar triangles is equal to the square of the ratio of their altitudes.

The vertices of a Delta ABC are A (-5,-1), B (3,-5) , C (5,2). Show that the area of the Delta ABC is four times the area of the triangle formed by joining the mid-points of the sides of the triangle ABC.

Prove that the two madians of a triangle divide each other in the ratio 2 : 1

The vertices of a Delta ABC are A(-5,-1) B(3.-5) , C-(5.2).Show that the area of the DeltaABC is four times the area of the triangle formed by joining the mid-points of the sides of the triangle ABC.

ZEN PUBLICATION-CO-ORDINATE GEOMETRY-ZEN ADDITIONAL QUESTIONS - SHORT ANSWER [SA] TYPE QUESTIONS
  1. Find the ratio in which (-4, 6) divides the line segment joining A (6,...

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  2. Find the points of trisection of the line segment joining the points. ...

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  3. Three vertices of a parallelogram are (a + b ,a - b ) , (2a + b, 2a - ...

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  4. A poin P divides the line segment joining A (3,-5) and B ( - 4, 8) wit...

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  5. If the midpoints of the sides of a triangle are (3, 4) (4, 6), and (5,...

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  6. In what ratio is the join of (-2, 2) and (4,5) cut by the axes of coor...

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  7. The vertices of DeltaABC are A (1, 2), B (4 ,6), and C (6, 14). AD bis...

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  8. Show that (1,-1) , (-2,2) , (4,8) and (7,5) are the angular points of ...

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  9. The line segment joining (3,-4) and (1, 2) is trisected by P(a,-2) and...

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  10. The centroid of a triangle ABC is ( 1, 2, 2) If the coordinates of A a...

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  11. The vertices of a Delta ABC are A (4,6), B (1, 5) and C (7,2). A line ...

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  12. Prove that the median of Delta ABC divides it into two triangles of eq...

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  13. Find the value of a for which the area of the triangle formed by A(a, ...

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  14. If a ne b ne0, prove that points (a, a^(2)), (b, b^(2)), and (0, 0) ca...

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  15. Prove that (a, 0), (0, b), and (1, 1) are collinear if (1)/(a) + (1)/(...

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  16. Find the values of a and b if P (9a-2,-b) divides the line segment A (...

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  17. The centre of a cicle is (2a, a -7). Find the values ofa if the circle...

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  18. For what value of k are (k, 2 2), (-k + 1, 2k), and (4-k, 6-2k) collin...

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  19. The vertices of a Delta ABC are A (-3,2) , B (-1,-4) and C (5,2) . If...

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  20. The vertices of a Delta ABC are A (-5,-1), B (3,-5) , C (5,2). Show t...

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