Amazing Diagonals Worksheet
How are the Diagonals in Special Quadrilaterals Related?
Materials Needed: 2 pairs of scissors, 4 rulers, 4 protractors
Directions: Work in groups of four
1. Each group member should have a rectangular piece of paper. Each of you should make a
different one of these quadrilaterals using paper folding and cutting:
Always start with your rectangular piece of paper so the short sides are parallel with the top of
your desk.
SQUARE:
 Fold your paper so that the top side of your rectangle lays evenly with the left side of the
rectangle.
 Cut off the excess paper at the bottom (along the dotted line below). When you unfold you
should have a perfect square
Fold
Cut
RHOMBUS:
 Fold you paper directly in half, folding the bottom of the rectangular paper up so the
bottom edge lays directly on the top edge.
 Keeping the folded edge at the bottom, fold your paper in half a second time. This time fold
it so that the left edge lands evenly on the right edge, keeping the fold to your left.
 Without unfolding, cut the smaller rectangle you made in half (along the dotted line below)
starting from the bottom right corner and cutting up towards the top left corner. When
you unfold you’ll have a perfect rhombus.
Fold
Fold
PARALELLOGRAM:
Fold your paper directly in half “hot-dog-style” then open it back up.
Fold your paper directly in half “hamburger style” then open it back up.
Mark the center where the two folds meet.
Fold the top edge of your paper down at a diagonal and fold the bottom edge of your paper
up at a diagonal so that the two edges meet perfectly right at the center point that you
marked.
 Open your paper back up and cut along those diagonal folds (along the dotted lines below)
that you created in the previous step. You should have a perfect parallelogram.




Fold
Fold
KITE:
 Fold your paper in half “hot-dog-style” with the fold on the left side
 Draw a dot along the right edge, 3 inches from the top
 Draw a straight line from the bottom left corner to dot and a straight line from the top left
corner to the dot.
 With your paper still folded, cut along the lines that you drew. Unfold the paper to reveal
your perfect kite.
Fold
2. The diagonal of a polygon is a segment joining two non-consecutive vertices.
Show that the square has each of these properties. Use a ruler and a protractor if necessary:
 The diagonals have the same midpoint
 The diagonals are perpendicular to each other
 The diagonals are equal in measure
Y
Y
Y
N
N
N
3. Decide whether each of the other quadrilaterals you made in step 1 has any or all of the
properties listed in step 2. The person who made the square should explore the properties of a
rectangle.
Rectangle
Rhombus
Parallelogram
4. Organize your results from step three in a quadrilateral chart.
Kite