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Given : X and Y are mid points of sides AC and BC of triangle ABC, respectively such that AX=CY
To Prove: (i) AC=BC
(ii) CX=CY
Proof: (i) Since X is the mid point of AC,
AX=CX=1/2AC ---(1)
Since Y is the mid point of BC,
BY=CY=1/2BC ---(2)
But AX=CY (Given)
=>1/2AC=1/2BC [Using (1) and (2)]
=>AC=BC
Hence, proved
(ii) AX=CY
=>CX=CY [Using (1)]
Hence, proved
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