Let R1 and R2 be reflections
in lines m1 and m2.
Let S1 and S2 be reflections
in lines n1 and n2.
·
R2 R1 = S2 S1 if
all 4 mirror lines are parallel and distance and direction from m1 to m2 is the
same as the distance and direction for n1 and n2. This product is a translation.
·
R2 R1 = S2 S1 if
all 4 mirror lines are concurrent and signed angle from m1 to m2 is the same as
the signed angle for n1 and n2. This product is a rotation.
How can we use this?
·
Fill in the
missing line. Given 3 parallel lines or
3 concurrent lines, find the fourth using this rule.
·
Triple product =
single line reflection for parallel or concurrent lines. Observe that R2 R1 = S2
S1 is equivalent to S2 R1 R2 = S1 or R2 R1 S1 = S2.