(1) Draw a line segment DE = 12cm.
Using a protractor,
Draw ∠EDF = 60° and ∠DEG = 45°.
Join DF and EG.
Taking D as the center and any radius,
Draw an arc,
Intersecting DE at H and DF at I.
Similarly,
Taking E as the center and any radius,
Draw an arc,
Intersecting DE at J and EG at K.
(2) Taking H as the center draw an arc of any radius greater than \(\frac{HI}{2}\).
Now,
Taking I as the center and the keeping the same radius,
Draw another arc,
Intersecting the previous arc at L.
Join and extend DL.
Similarly,
Taking J as the center draw an arc of any radius greater than \(\frac{JK}{2}\) .
Now,
Taking K as the center and the keeping the same radius,
Draw another arc,
Intersecting the previous arc at M.
Join and extend EM,
Intersecting extended DL at A.
(3) Taking D as the center and radius greater than \(\frac{AD}{2}\),
Draw arcs on each side of AD.
Now,
Taking A as the center and same radius,
Draw arcs,
Intersecting the previous arcs at points N and O.
Join and extend NO.
Extended NO intersects line segment DE at point C.
Join AC.
Similarly,
Taking E as the center and radius greater than \(\frac{AE}{2}\),
Draw arcs on each side of AE.
Now,
Taking A as the center and same radius,
Draw arcs,
Intersecting the previous arcs at points P and Q.
Join and extend PQ.
Extended NO intersects line segment DE at point B.
Join AB.
(4) ∆ABC is the required triangle.
