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Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.
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Solution
Given, X is the mid-point of AC
AX = CX = `1/2` AC
⇒ 2AX = 2CX = AC ...(i)
And Y is the mid-point of BC.
BY = CY = `1/2` BC
⇒ 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 equation (iii), 2AX = 2CY
⇒ AC = BC ...[From equation (i) and (ii)]
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