Construct a ABC such that AB = 5 cm. A = 45° and the median from A to BC is 4 cm.

Steps of construction:

Step 1: Draw a line segment AB = 5 cm

Step 2: Draw BX such that ∠ BAX = 45°

Step 3: Draw AY ⊥ AX.

Step 4: Draw the perpendicular bisector of AB intersecting AY at O and AB at M.

Step 5: With O as center and OA as radius, draw the circle.

Step 6: With M as center, draw an arc of radius 4 cm meeting the circle at C and at C’.

Step 7: Complete the Δ ABC which is the required triangle.