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Axioms are assumed

Solve the following question using the appropriate Euclid's axiom:
In the figure,we have $BX = \frac{1}{2} AB$,$BY = \frac{1}{2} BC$ and $AB = BC$.
Show that $BX = BY$.

$A$ solid has.........

If $P$,$Q$,and $R$ are three points on a line,and $Q$ lies between $P$ and $R$ [see figure],then prove that $PQ + QR = PR$.

Ram and Ravi have the same weight. If they each gain weight by $2\, kg$,how will their new weights be compared?

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