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A diagonal of parallelogram divides it i...

A diagonal of parallelogram divides it into two congruent triangles.

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`"Suppose ABCD is parallelogram and BD is the diagonal, then there are 2 triangles;"`
`/_\ABD and /_\CBD`
`AB=CD and AD=BC ("opposite sides of a parallelogram are equal")`
`BD " is the Common Side"`
`therefore /_\ABD cong /_\CBD(" By SSS Congruency")`
`"hence the given statement is true"`
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Knowledge Check

  • Prove that each of the diagonals of a parallelogram divides it into two congruent triangles .The following steps are involved in proving the above result .Arrange them in sequential order . (A) By SSS congruence property , DeltaDAB~=DeltaBCD . (B) Let ABCD be a parallelogram and join BD . ( C) AB=CD,AD =BC (opposite sides of the parallelogram ), and BD =BD(common side) (D) Similarly ,AC divides the parallelogram into two congruent triangles .

    A
    ABCD
    B
    BCAD
    C
    BACD
    D
    CBAD

  • 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

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