Prove that the diagonals of a parallelogram divide it into two congruent triangles.
Given : A ||gm ABCD
To prove :
Construction : Join AC
Proof : Since ABCD is a ||gm
AB||DC and AD||BC
Now AB||DC and AC is a transversal
DCA = BAC [alt. interior angles]
Again AB||DC and AC is the transversal
Hence diagonals of a ||gm divide it into two congruent triangles.
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