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

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B

Instead of drawing the perpendicular bisector of line segment BC, we’ll draw the angle bisector of angle B in this case

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C

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.

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D

None of the above

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Solution

## The correct option is C 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.

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