Another approach to this would be to draw a line away from the triangle and use the "Properties: Connections" inspector to turn off "Allow connections to other objects." Then you can drag the line over the triangle and position it and its endpoints without the line attempting to connect to the triangle.
If you usually don't want your lines to attempt to connect to shapes, you can select the line tool by Option-clicking it, or clicking and holding the line tool to get the tool menu, and choose "Inspect Style" from that menu. Then the inspectors will reflect the tool, and you can go and turn off "Allow connections to other objects." Then future lines will not try to connect to objects unless you draw the line and then turn that attribute back on.
The reverse approach would be to disable connections to the triangle. This is done by selecting the triangle, then unchecking the "Allow connections from lines" checkbox in the "Properties: Connections" inspector. Then you will be able to draw lines on the triangle without them attempting to connect to the triangle. However, I think this probably is not as good a match for your usage as the approach above.
Another approach, which would take more effort up front but which might be easier long-term, would be to edit the magnets on the triangle to place a magnet on each side of the triangle (or your case, two magnets on each side, splitting the triangle into thirds), then draw lines connecting those magnets. This has the benefit of being very flexible: if you subsequently resize the triangle, the lines trisecting the triangle will resize and shift as appropriate. To edit the magnets, use the Magnet tool, and/or use the magnets popup in the "Properties: Connections" inspector. The inspector popup has a setting for "two magnets per side," which may be exactly what you're looking for in this case. (Note that with certain line types, this can be a bit fiddly, and if you have auto-layout turned on, you're likely to be fighting it.)
One final alternative is to hold down the Option key while drawing the line - this will prevent the line from attempting to connect to any shapes. (Use with the Shift key to keep your lines horizontal or vertical.)