using  ruler  and compass only:
.construct triangle ABC ,having given BC=7cm, AB-AC=1 cm and angleABC=45degrees.
 

Step 1: draw the line segment BC= 7cm.

at point B, draw an angle of 45 degree 

Step 2: Now, draw an arc on AB and mark that point D , such that BD= 1 cm.

Step 3: Join CD and draw a perpendicular bisector PQ of CD. It intersect BX at A point.

Step 4: Join AC. 

thus, ΔABC is a required triangle