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In the adjoining figure , we have X and...

In the adjoining figure , we have X and Y are the mid - point of AC and BC and AX = CY . Show that AC =BC.

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Given , X is the mid - point of AC.
`:. AX=CX= (1)/(2)AC`
`rArr ` 2AX=2CX=AC ...(i)
and Y is the mid -point of BC.
`:. BY=CY=(1)/(2)BC`
`rArr` 2BY=2CY=BC ...(ii)
Also, given AX=CY ...(iii)
According to Euclid's axiom, things which are double of the same things are equal to one another.
From Eq. (iii), 2AX=2CY
`rArr` AC=BC ["from Eqs. ("i) and (ii)"]
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