(Polar molecules, Non-polar molecules, etc.)
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The dashed line and the wedge/solid triangle are merely drawn to the portray that the molecule is three dimensional. The dashed line usually shows that the bonded pair is going into the plane of the page and the wedge is going out of the plane of the page. Use them when the molecule cannot be drawn in two dimensions.
I believe the lines and triangles you are referring too are just bonds between two atoms. The lines and triangles symbolize depth. If you imagine your paper to be the plane you're drawing the VSEPR structure on, the lines fading out would indicate an atom that is going into your paper, and the triangle would indicate an atom that was coming out of the paper.
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