In the Fig.5.5, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

Given, X is the mid-point of AC

AX = CX=

⇒ 2AX =2CX = AC …(i)

Y is the mid-point of BC.

BY = CY =

⇒ 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)]