If $A M$ and $C N$ are perpendiculars on the disgonal $B D$ of a parallelogram $A B C D$ ,Is $△ A M D ≅ △ C N B$ ?Give reason.

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Solution

In triangles $A M D$ and $C N B$
$A D = B C$ (opposite sides of a parallelogram)
$∠ A M B = ∠ C N B = 90^{\circ}$
$∠ A D M = ∠ N B C$ since $A D ∥ B C$ and $B D$ is the transversal.
So, $△ A M D ≅ △ C N B$ by AAS

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