Why and how does this active band pass filter change a triangle form to a sine form? I know that the band pass filter consists of a low pass and a high pass , so it cancels out some frequencies , but I don't understand graphically how this could happen.
Any repeating wave form - including a triangle wave - can be represented as a sum of sine waves. Look up "Fourier analysis" for details. These sine waves consist of a "fundamental", the lowest frequency, plus a series of "harmonics" at higher frequencies.
Applying a bandpass filter to the waveform just selects the frequency you want, and discards all the others. Pick the right filter and, in theory at least, you'd get a perfect sine wave out.