I am using RegionIntersection[]
to intersect two rectangles, phrased
as Polygon[]
s:

RegionIntersection[]
returns an incorrect result (the green region above; detail below),
and issues a series of error messages:

Here is the region returned as the intersection, which is not correct (it should be a quadrilateral):
Polygon[{{0.407273, 0.650444}, {0.509656, -0.0200315}, {0.998507,
0.0546171}, {0.640904, 0.767621}, {0.998507, 0.0546171}}]
Here it is as a line drawing:

Here is the originating call that produces the incorrect intersection:
RegionIntersection[
Polygon[{{0.5096555454081809`, -0.02003146973392257`}, \
{0.9985073695269602`, 0.05461714932464575`}, {0.6966031018052412`,
2.0316992956026936`}, {0.2077512776864619`,
1.9570506765441251`}}] ,
Polygon[{{0.9985073695269602`,
0.05461714932464575`}, {0.6409040075686694`,
0.767621034809768`}, {-1.1468443539373534`, \
-0.12901478643123643`}, {-0.7892409919790626`, -0.8420186719163586`}}]
]
Can anyone see what's going on?