Question

Using ruler and compasses only, construct a ΔABC 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° and `∠`EYX = `∠`C = 60°
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
∴Δ ABC is the required triangle