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Construct a triangle ABC in which BC =8 cm, ∠B = 45° and AB – AC = 3.5 cm.

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Steps of Construction

 (i) Draw BC = 8 cm. 

(ii) Construct  ∠YBC = 45°.

 (iii) From ray BY, cut-off line segment BD = 3.5 cm. 

(iv) Join CD. 

(v) Draw perpendicular bisector of CD intersecting BY at A.

 (vi) Join AC to obtain the required triangle ABC.

Justification 

As A lies on the perpendicular bisector of CD. Therefore, 

AD = AC

 Now, BD = 3.5 cm 

⇒     AB – AD = 3.5 cm 

⇒     AB – AC = 3.5 cm

Hence, △ABC is the required triangle.

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