Mira paper folding

1. Basic constructions
using Mira, Paper Folding,
Compass and
Straightedge.
REPORTED BY: JEFF JASPER A. NIEDO

2. 1. Mira – is the commertial name given to a piece of
colored transparent plastic used to reflect geometric
objects.
Copy a segment
Place the Mira on your paper not intersecting the
given segment. Looking through the Mira, you will
see the segment reflected on the other side.
Using your pencil, trace the reflected copy behind
the |Mira.

3. Find reflection over a given line
Place the Mira on the given line of reflection. Look
through the Mira to see the reflection on the other
side. Using your pencil, trace the reflected image on
the other side of the Mira, producing the reflection in
the given line.

4. Find the line reflection
Place the Mira between the segment. While
looking through the Mira, move the Mira
until the left segment’s reflection aligns with
the right segment (behind the Mira). The
Mira shown here needs to be moved a bit
more to get alignment. When aligned, trace
along the bevelled edge of the Mira to get
the reflection line.

5. 2. Paper
Folding/Patty paper –
patty paper is a semi-transparent dry waxed
paper sold in rectangular sheets. If you write
on one side of the paper, you will be able to
see your writing through the backside of the
paper, as well as see other images through
the paper.

6. Construct a bisector of a segment
STEPS:
1. Using a straightedge, draw the line segment AB on
the Patty.
2. Fold the patty paper such that point A and B
coincide with one another.
3. Crease the paper along this fold.
4. Open the paper and using your straightedge, draw a
line along the crease.
5. The crease line is the bisector of the segment.

7. Construct an angle bisector.
STEPS:
1. Using your straightedge, draw the angle ABC
on the paper.
2. Fold the patty paper such that the ray BA
coincides with the ray BC
3. Crease the paper along this fold
4. Open the paper and using your straightedge,
draw a line along the crease.
5. The crease line of the line of reflection which
will be the bisector of the angle.

8. Construct a perpendicular from
a point not a line.
STEPS:
1. Using your straightedge, draw line m and point p, not
on the line, on the patty paper.
2. Fold the patty paper such that two parts of the line m
will lie exactly on the top of one another.
3. Position the paper such that the point p will lie on
this fold.
4. Crease the paper along this fold.
5. Open the paper and using your straightedge, draw a
line along the crease.
6. The crease line is the line from p perpendicular to
line m.

9. 3. Compass and
Straightedge – a compass
and straightedge can be used to
draw many geometric figures and
construction.

10. Copying a line segment
STEPS:
Construct a copy of line segment AB
1. Draw point C.
2. Place the compass point on a and the pencil end on point b.
3. Without changing the compass width, place the compass point c
and draw an arc.
4. Draw point d, the other end point of the copied line segment,
anywhere on the arc. Draw a line segment from c to d with a
straightedge. Line segment cd should have the same length as ab
as long as the compass width was maintained.
5. You can pick any point on the arc constructed in step 3 to copy
line segment ab.

11. Bisecting an angle
STEPS:
Construct an angle bisector.
1. Place the compass point on vertex e and draw an arc through
both ray ed and ef.
2. Place the compass point on the intersection of the arc and
ray ef, draw an arc in the interior of angle def. Maintain the
width of the compass and repeat this process with the
compass point instead on the intersection of the arc and ray
ed. Make sure the two arcs drawn in this step intersect.
3. Label the intersection of the two interior arcs g. draw a ray
from e through g. Ray eg should bisect angle def forming
congruent angles deg and feg.