Question

Using ruler and compasses only, construct a ∆ABC from the following data: AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Answer 1

Steps of construction: 

Step 1: Draw a line segment XY of 12cm. 

Step 2: Draw ∠DXY = ∠B = 45^o and ∠EYX =  ∠C = 60^o 

Step 3: Draw the angle bisectors of angles of DXY and EYX which intersects each other at A. 

Step 4: Draw the perpendicular of AX and AY which intersect XY at B and C respectively. 

Step 5: Join AB and AC 

∆ABC is the required triangle