I think the four closest synonyms for rays are: Beam, streak, glare, or column of light.
It depends on what kind of rays you are suggesting then it could be; bar, blaze, blink, emanation, flash, flicker, gleam, glimmer, glint, glitter, hint, incandescence, irradiation, light, moonbeam, patch, pencil, radiance, radiation, scintilla, shaft, shine, spark, sparkle, streak, stream, sunbeam, trace, wave, beacon, chink, column, dartle, emission, finger, glare, glow, laser, radiation, shaft, shimmer, shoot, twinkle
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Four rays since it is a quadrilateral.
Perpendicular rays are two rays that intersect one another to form four right angles. Below is an image that shows two perpendicular rays.
<----.----> <---------. .----------> Those are the Rays in a line, or segment
I don't think there are rays of naming. Angles are made up of 2 rays.
They could be the four sides of a square.