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Each diagonal of a ||gm divides it into ...

Each diagonal of a ||gm divides it into two triangles of the same area

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A diagonal of a parallelogram divides it into two triangles of equal area.

A diagonal of a parallelogram divides it into two triangles of equal area. GIVEN : A parallelogram A B C D in which B D is one of the diagonals. TO PROVE : ar ( A B D)=a r( C D B)

Knowledge Check

  • Asserion (A) : The diagonals of a ||gm divide it into four triangle of equal area. Reason (R ) : A diagonal of a ||gm divides it into two triangle of equal area.

    A
    Both Assertion (A) and Reason (R ) are true and Reason (R ) is a correct explansion of Assertion (A).
    B
    Both Assertion (A) and Reason (R ) are true but Reason (R ) is not a correct explansion of Assertion (A).
    C
    Assertion (A) is true and Reason (R ) is false.
    D
    Assertion (A) is false and Reason (R ) is true.
  • Assertion (A) : If ABCD is a rhombus whose one angle is 60^(@) then the ratio of the lengths of its diagonals is sqrt3 : 1 Reason (R ) : Median of a triangle divides it into two triangle of equal area.

    A
    Both Assertion (A) and Reason (R ) are true and Reason (R ) is a correct explansion of Assertion (A).
    B
    Both Assertion (A) and Reason (R ) are true but Reason (R ) is not a correct explansion of Assertion (A).
    C
    Assertion (A) is true and Reason (R ) is false.
    D
    Assertion (A) is false and Reason (R ) is true.
  • The median of a triangle divides it into two

    A
    triangles of equal area
    B
    congruent triangles
    C
    right angled triangles
    D
    isosceles triangles
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    Show that a median of a triangle divides it into two triangles of equal area.

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    Median divides a triangle into two triangles of the same area

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

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