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Show that the diagonals of a parallelog...

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

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P is mid point of AC and BD
AP=PC
PB=DP
`/_APB and /_DPC`
AP=PC
PB=PD
AB=DC
area of `/_APB`=area of `/_DPC`
...
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Knowledge Check

  • Show that each diagonal of a parallelogram divide it into two congruent triangles. The following are the steps involved in showing the above result. Arrange them in sequential order. A) In triangleABC and triangleCDA , AB=DC and BC=AD (therefore opposite angles of parallelogram) AC=AC (common side). B) Let ABCD be a parallelogram. Join AC. C) By SSS congruence property, triangleABC ~=triangleCDA . D) Similarly, BD divides the triangle into two congruent triangles.

    A
    BACD
    B
    BDAC
    C
    BADC
    D
    BDCA

  • 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.

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