​
​Show is not suitable for combine 2D and 3D graphics .
But there are many other features in Mathematica.
I recommend all objects to create in 3D space and use only Graphics3D,
EG :
In[]:=
​​obj1={Blue,Triangle[{{1,1,1},{1,2,3},{-1,4,1}}]};​​obj2={Green,Triangle[{{2,1,0},{1,4,0},{4,4,0}}]};​​obj3={LightPink,InfinitePlane[{{1,0,-0.5},{1,1,-0.5},{0,0,-0.5}}]};​​Graphics3D[{Opacity[0.7],obj1,obj2,obj3},​​Axes->True,AxesLabel->{"X","Y","Z"},​​PlotRange->{{-1,5},{-1,5},{-1,3}}]
Out[]=