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Osterhaus, S.A. (1998) Braille/Print Protractor teacher's guide. Louisville, KY: American Printing House.

by Susan A. Osterhaus

It is often necessary to measure and draw angles in the geometry classroom as well as every day situations. The most common device for measuring angles is a protractor, usually in the shape of a semicircle. The semicircular edge of the protractor is marked with evenly spaced divisions from 0o to 180o. Simply adding dots to the commercially available product doesn't facilitate its use by a blind user. However, another instrument for measuring angles exists, and it is called a goniometer. Geologists use a goniometer for measuring crystal angles, and physical therapists use one for measuring movement at a joint. A goniometer (protractor with a wand) when adapted provides a very user-friendly angle measuring and drawing device for both blind and sighted users.

The Braille/print adapted protractor has several features that make it easier to use than most adapted protractors currently available. Bold large print numbers and two Braille dots are used to mark degrees at 10o increments. A single dot represents those increments ending in the numeral 5 (with the exception of the 45o, 90o, and 135o which have three dots for quick reference). Probably the most important feature however, is the wand which is attached to the "center" of the semicircle's diameter. When the pointed end of the wand is aligned with a degree measurement, the corresponding angle is formed by the extended straightedge of the wand and the edge (diameter) of the protractor. An additional bonus is that the desired angle's supplement is also formed, allowing a significant teachable moment. Other attractive features are its size and plastic flexibility; it can easily be used to measure most angles in textbooks - even ones close to the binding. Furthermore, this protractor can be used independently to both draw and measure angles.

The recommended procedure for using this protractor consists of the following steps:


  1. Examine the drawn angle to determine roughly whether it is acute, obtuse, or possibly a right angle and as a check after the final measurement.
  2. Loosen the screw positioning the wand, and with both hands form an angle and tentatively align the edge of the protractor and the edge of the wand (making sure that the pointed end is located on top of the protractor) with the respective rays of the provided angle - being sure that the two vertices are aligned as well. Tighten the screw somewhat; fine-tune; and then tighten completely.
  3. The pointed end of the wand will be aligned with the angle's measure. Read the measurement directly in print or begin counting from either end of the protractor's edge (diameter) until the tip of the wand is reached. At this point, check yourself to be sure that you have the angle's measurement and not its supplement. If you completed step 1, you will know. Practice also improves speed and allows short-cuts.


  1. If the plan is to copy a drawn angle using a protractor, then go through Steps 1 - 3 listed above. If the task is simply to draw an angle with a designated measure, carefully align the pointed end of the wand with that measurement and tighten the screw completely.
  2. Place the protractor on the desired drawing surface - plain unlined paper for a visual result or Braille paper on a hard rubberized surface (The Sewell Raised-Line Drawing Board is well-suited for the task.) for a raised-line drawing. Firmly hold the protractor in place with the fingers of one hand - making sure the thumb is holding down the wand securely.
  3. Draw the angle formed by the edge of the protractor and the edge of the wand (being sure to define the vertex) using a print writing instrument for a visual result or an appropriate raised-line tool for a tactile graphic: The Sewell drawing stylus is very easy to hold and manipulate. Line tools 3 and 6 from the APH Tactile Graphics Kit also work well. However, an ordinary pencil or ball point pen may be the best and most easily accessible tool to use.