Answers:

(i) False

If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

(ii) True

ABC is a triangle with M, N

DE is expanded to F such that EF = DE

AE = EC (E is the mid-point of AC)

DE = EF

AED = CEF (Vertically Opposite angle)

By SAS criterion,

∆ADE ~ ∆CEF

CF = AD (CPCT)

BD = CF

∠???????????? = ∠????????????

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AD ‖ CF and BD ‖ CF

When two sides of a quadrilateral are parallel, then it is a parallelogram

∴ DF = BC and BD ‖ CF

∴BDFC is a parallelogram

DF = BC

DE + EF = BC