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Just use implicit_plot:

p, t= var('p t') 
a=(-2*p*t^2-p^2*t)+(2*t*p-p^2)+t+1 
b=(p*t^2+2*p^2*t)+(2*t*p-t^2)-p+1 
c=(p*t^2-p^2*t)+(t^2+2*t*p+p^2)+t-p #3 sides (a,b,c) in terms of theta and phi
R = region_plot([a+b>=c, b+c>=a, c+a>=b], (t,-2,2), (p,-2,2))
C = implicit_plot(t*p*(t-p)+t*p+2*(t-p)-1,(t,-2,2), (p,-2,2),color='red')
show(R+C)