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Tuesday
Before we turn to congruence we need to address a few things:
1. Composition of rotation and translation
2. Composition of three reflections
3. Composition of two rotations with different centers
4. Conjugates of isometries
5. A composition of any number of isometries reduces down to at most three.
6. Problems from below
7. Drama club
Question 8.1. Prove or disprove: Every translation is a product of two rotations.
Question 8.2. Prove or disprove: Every translation is a product of two non-involutory
rotations.
Question 8.3. If P = Q, then there is a unique translation taking point P to point Q, but
there are an infinite number of rotations that take P to Q.
Question 8.4. Show that rn rm rl = rl rm rn whenever lines l, m, n are concurrent or have a
common perpendicular. What happens when they are not?
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