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Answer:
Euclid's first and second axioms are used.
Step-by-step explanation:
Euclid's first axiom : Equality is transitive.
i.e, If x = y, and if y = z, then x =z.
Euclid's second axiom : Addition of equals.
If x =y and a = b, then x + a = y + b.
Given:
BC = XD
C is the mid point of AB => AC = BC
D is the midpoint of XY => XD =YD
To prove :
AB = XY
Proof :
Since equality is transitive, we have
AC = BC = XD = YD
Also, using axiom of addition of equals we have
AB + BC = XD + YD
AC = XY
Hence proved.
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