Question

to construct a triangle given its base a base Indian and the difference of the other two sides ​

Answer 1

Solution

Given ,

• the base BC a base angles CB and the difference of other two side AB-AC or AC-AB .

Required ,

• to construct the triangle ABC

There are following two cases

Case (i) Let AB > AC i.e. AB-AC is given .

Steps to construct ,

• draw the base BC and at point B make an angle say XBC equal to the given angle .
• cut the line segment BD equal to AB-AC from the ray BX.
• join DC and draw the perpendicular bisector say PQ of DC .
• let it intersect BX at a point A. join AC .

Then , ABC is a required Triangle.

Case (ii) Let AB< AC i.e. , AC - AB is given .

Steps to construction ,

• draw the base BC and at point B make an angle , say XBC equal to the given angle .
• cut the line segment BD equal to AC - AB from the line BX extended on opposite side of line segment BC .
• join DC and draw the perpendicular bisectors say PQ of DC
• let p q intersect BC at point A. join AC .

Then , ABC is a required Triangle

Justification ;

base BC and CB are drawn As given .

• the point a lies on the perpendicular bisector of DC .
• AD = AC

So, BD = AD - AB = AC - AB