Question

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

• A. Instead of having B as the base angle, have the same construction with C as the base angle
• B. Instead of drawing the perpendicular bisector of line segment BC, we’ll draw the angle bisector of angle B in this case
• C. Instead of plotting the point D on the ray BX as (AC – AB) = say 2 units, 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.
• D. Instead of having B as the base angle, have the same construction with A as the base angle

Answer 1

The correct option is C

Instead of plotting the point D on the ray BX as (AC – AB) = say 2 units, 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.