It's easy to rotary cut patchwork shapes for quilts. Nearly all of the shapes used in quilts can be cut from long, rotary cut strips of fabric with the straight grain running along the edges of the strips.
How to Cut Squares and Rectangles
 Squares have four 90degree angles (right angles) and four equal sides.
 True rectangles have four right angles and are twice as long as they are wide.
 Longer rectangles are sometimes called bars.

Cut Long Strips
To cut a square, rectangle, or bar, start by cutting long strips of fabric that are 1/2" wider than the height of the finished shape.

Square End of Strip
Square up one end of the strip.

Cut Segments
Starting at the squared up end, use rotary equipment to cut away segments that are 1/2" longer than the finished patch length.
Cutting Tips
 Keep patch angles accurate by carefully aligning the ruler line used to measure the width of the patch with the leading edge of the fabric. Choose any horizontal ruler line and align it to the bottom of the strip before cutting. When both a horizontal and vertical line match, you'll have an accurate cut.
 Hundreds of specialty rulers are available for rotary cutting but you'll do just fine with the basics. Add specialty rulers after you've become more accustomed to the technique and know which types of cuts you will make most often.
 You could also opt to purchase a cutting system. AccuQuilt is one company that makes cutters.
 Remember all rotary cutting safety guidelines as you position fabrics to make cuts.
 Lefthanded cutters must reverse fabric and ruler positions for many cuts.
How to Rotary Cut Half Square Triangles
Triangles have three angles and three sides, and that means at least one edge of every triangle is cut along the fabric's stretchy bias. Handle triangles carefully to avoid stretching them out of shape.
A good portion of the triangles you'll use in your quilting projects are quick pieced, which means you won't have to fool with stretchy bias edges, but there are times when it's necessary to cut individual patches.
Let's start with half square triangles, one of the most commonly used quilting shapes.

Cut Square
Cut a square that's 7/8" longer and wider than the finished length of the short sides of the triangle.

Cut in Half Diagonally
Use your rotary equipment to cut the square in half diagonally, producing two half square triangles with the straight grains parallel to their short edges.
Half square triangles are used to make corner triangles for a quilt when quilt blocks are sewn on point.
How to Cut Quarter Square Triangles
Quartersquare triangles look exactly like half square triangles, but they're very different. The fabric's straight grain runs parallel to the longest edge of a quartersquare triangle. The straight grain runs along the short edges of half square triangles.
Quartersquare triangles are used in many quilt blocks, but we usually sew with quickpieced units that eliminate the need for individual triangles.
Quarter squares are also used as setting triangles along the sides of an onpoint quilt. That configuration puts their sturdy straight grain edges on the perimeter of the quilt.
Using half square triangles in the outermost position would result in a quilt with stretchy bias edges on its perimeter, not a good thing since you want quilt edges to stay as stretchfree as possible.

Cut Square
Cut a square with sides that are 11/4" longer than the finished length of the triangle's longest edge.

Cut in Half Twice
Use your rotary equipment to cut the square in half twice diagonally.
How to Rotary Cut Long Triangles
Scalene triangles have three unequal sides. The scalene triangle we use most often in quilting is the right scalene triangle, commonly called a long triangle.
To cut patchwork that's twice as long as it is wide:

Cut Strip
Cut a strip of fabric 11/16" wider than the finished length of the long triangle's shortest side. Estimate as best you can if your rotary ruler isn't marked in 16thinch increments—it's better to cut a little wider than to cut a little smaller.

Cut Rectangle
Cut a rectangle from the strip that's 5/16" longer than the finished length of the long triangle.

Cut Diagonally
Cut the rectangle once diagonally to produce two triangles with the straight grain parallel to their straight edges.

Cut Diagonally Once More
To make long triangles that are mirror images of the first pair, cut another rectangle diagonally, but this time cut along the opposite corners. See the illustration above.
How to Cut Long Triangles From Bars

Draw Triangle
Draw a finished size long triangle on graph paper and add a 1/4" seam allowance to each side. Measure.

Cut Parent Strips
Cut parent strips to match the measured height. Cut bars from the strip to match the measured length.

Divide Bars
Divide the bars diagonally.
How to Cut Equilateral Triangles
Equilateral triangles are the same length on each side, with 60degree angles at each of their three corners. They are used in many quilts, including the traditional 1000 Pyramids design.

Measure Midpoint to Tip
Using the finished size, measure the distance from the midpoint of a triangle's base to the tip of the point above it.

Add Length and Cut
Add 3/4" to the measurement and cut a fabric strip of that width.

Align Line
Align the 60degree line of a rotary ruler with the long edge of the fabric strip as shown above.

Cut
Cut along the right edge of the ruler to establish the first edge of the triangle. Discard the piece you cut off or throw it in your scrap bag.

Rotate Ruler
Rotate the ruler, aligning its other 60degree line along the bottom edge of the strip. The edge of the ruler should be positioned to form a point at the bottom edge of your first cut.

Cut Along Side of Ruler
Cut along the right side of the ruler to create a triangle. Measure it. All three legs should be the same length7/8" longer than the triangle's finished size.

Continue
Continue flipflopping your ruler to cut more equilateral triangles. Check their dimensions occasionally to make sure the angles and leg lengths are still accurate.
How to Cut Diamond Shapes
A diamond is basically a squished square. It has four sides of equal length, but its corners are no longer at 90degree angles. Quilt patterns commonly call for diamonds with 30degree, 45degree or 60degree angles at their narrow points.
All three types of diamonds are cut from strips of fabric that are 1/2" wider than the finished height of the diamond.

Cut Strip
Cut a strip of fabric that's 1/2" wider than your diamond's finished height.

Align Ruler
Align the ruler's 30degree, 45degree, or 60degree line with the left lower edge of the fabric, sliding it far enough onto the strip so that there's fabric under its entire right edge.

Rotary Cut
Rotary cut along the right edge of the ruler to create the diamond's first angled side.

Match Line With Edge
Find the line on your rotary ruler that matches the cutting height of the diamond—the same line you used to cut the fabric strip. Match the line with the angled left edge of the fabric and align the degree line along the bottom edge of the strip.

Rotary Cut Again
Rotary cut along the right side of the ruler to cut away the first diamond. Continue cutting diamond segments as needed for your quilt.