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Step-by-step explanation:
In the triangles ABC and CDA, we have
AB = CD ( opposite sides of rectangle )
BC = DA ( opposite sides of rectangle )
AC = CA ( common )
Therefore, ∆ABC is congruent to ∆CDA ( By SSS congruence criteria )
Therefore, Angle CAD = Angle ACB ( CPCT )....(1)
Now, in triangles ADN and BCM, we have,
Angle AND = Angle CMB ( each of 90°)
Angle NAD = Angle MCB ( Proved in (1) )
AD = CB ( opposite sides of rectangle )
Therefore, ∆ADN is congruent to ∆BCM ( by AAS congruence criteria )
Therefore, side AN = CM ( CPCT )
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