Construct a ABC in which BC = 4.5 cm, B = 45o and AB - AC = 2.5 cm. Justify the construction.
Steps of construction:
i) Draw a ray BX and cut off a line segment BC = 4.5 cm from it.
ii) Construct XBY = 45o.
iii) Cut of a line segment BD = 2.5 cm from ray BY.
iv) Join CD.
v) Draw perpendicular bisector of CD cutting BY at A.
vi) Join AC.
ABC is the required triangle.
Point A lies on the perpendicular bisector of DC. Therefore, AD = AC
So, BD = AB - AD = AB - AC
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