I am a newbie quilter.... so I still have the instructions for this ruler. I know that the half-square triangle works just like Thangles, if you have ever tried those. I will type out the instructions below... hopefully it will help.
NOTE: Cutting guide marks on the ruler are for finished-size triangles.
CUTTING QUARTER SQUARE TRIANGLES
Quarter-square triangles are cut so the hypotenuse (long side) of the triangle is on the fabric straight of strain.
1. Select black line on ruler that corresponds to the desired finished size of the hypotenuse of triangle. Solid lines are for even inches and dashed lines are for 1/2" increments.
2. Follow across the line to the right edge of the ruler and cut a fabric strip the width indicated. For example, to cut a 4"-finished quarter-squaqre triangle, cut a 2 1/2" wide strip.
3. Cut triangles as shown, first placing the cutting guidelines along the bottom cut edge of strip and then along the top edge of strip (Photo A) (The photo shows the triangle placed on the strip so that the hypotenuse is first on the bottom and then next flipped to the top and so on. )
CUTTING HALF-SQUARE TRIANGLES
Half-square triangles are cut so the legs (short sides) of the triangle are on the fabric straight of grain.
1. Select yellow line on ruler that corresponds to the desired finished size of the legs of triangle.
2. Follow across the line to the left edge of the ruler to find the width to cut fabric strip. Cut a strip this width. For example, to cut a 4" finished half-square triangle, cut a 4 1/2" wide strip.
3. Cut triangles as shown, first placing the cutting guideline along the bottom cut edge of strip and then along the top edge of strip (Photo B) The yellow shaded area of the ruler will extend beyond the edge of the strip. (The photo shows the triangle with the hypotenuse at a 90 degree angle to the fabric and the little tiny yellow triangle is placed right above the top of the strip. Then the triangle is flipped for next cut.)
In the first photo - Quarter-squre triangles, the cuts end up looking like ric rac.... every cut is angled. In the second photo, for the Half-square triangles, the first cut is vertical and the second is diagonal, then vertical and then diagonal and so on.
They give a tip for the Half-square triangles: Your triangles will be pre-trimmed with the tiny fabric tips that you normally cut off after sewing already eliminated [on one side]. We like to cut these triangles with our strip folded in half so half our triangles are trimmed on the right end and the other half on the left.
I hope that this makes sense without the photos for help. If you need me to, I can try to attach the photos, or I can take a picture with my phone and send it in a text.