Question:
In the adjoining figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.
Solution:
Given, X is the mid-point of AC
AX = CX = ½ AC
=> 2AX =2CX = AC ……(i)
and Y is the mid-point of BC.
BY =CY = ½ 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 Eq. (iii), 2AX = 2CY
=> AC = BC [from Eqs. (i) and (ii)]