Given a base angle B and the difference of the sides AC and AB (not necessarily in this order), what is the difference in the steps of constructions when
i) AC > AB
ii) AC < AB
Instead of plotting the point D on the ray BX as (AC – AB) = say 2units, we rewrite it as (AB – AC) = -2 units and plot the point D 2 units down south of point B on the same ray BX.
We have two things in common in both the constructions; the base length BC and the base angle B.
If we take the first construction into consideration, we are also given (AB – AC) and that AB > AC and in that case we mark BD = (AB – AC) = say, 2 units on the ray BX and then join D to C and continue with the construction.
If we take the second construction into consideration, we are given (AC – AB) and that AC > AB and in this case we will first rewrite it to (AB – AC) = -2 units which means that the line segment BD will be on the same ray BX but just that it will be constructed 2 units below the point B but on the same ray BX .
And the rest of the construction is same as that of the previous construction.