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

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Sol:

Steps of construction:

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

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

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

Therefore  Δ ABC is the required triangle

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