Math 5270 Transformational Geometryemina/teaching/5270s13/5270_Day5_notes.pdf · Day 5, Summer 13...
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Math 5270Transformational Geometry
Day 5
Summer 13
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Composition of rotations
Composing rotations about the same point yields a rotation.
Such rotations commute.
Composing rotations about different points yield a rotation...
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Composition of rotations
Composing rotations about the same point yields a rotation.
Such rotations commute.
Composing rotations about different points yield a rotation...
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Use your geogebra to
Make an angle slider for angle α between 0◦ and 360◦
In input bar write β = 360◦ − α
Pick any two points A and B and observe the composition of
rotation about A by α, followed by rotation about B by β.
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Group of rotations R?
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Equation for the rotation not around the origin?
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Alternative?
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How can we tell two isometries are the same?
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Reflections
Definition
wthout coordinates
with coordinates
Hmm... I think I might need more space...
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Reflections
Definition
wthout coordinates
with coordinates
Hmm... I think I might need more space...
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Equation for a reflection
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Equation for a reflection, take 2
Any super easy reflections you know?
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Fixed points, fixed sets?
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What happens when you compose two reflections?
Use your geogebra to observe what happens when you compose
different reflections.
Why did I say different?
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Group of reflections?
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Every isometry is a composition of reflections!
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Some of students’ work
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Congruence...
CCSS.Math.Content.HSG-CO.B.7 Use the definition of
congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent.
CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for
triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
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Congruence...
CCSS.Math.Content.HSG-CO.B.7 Use the definition of
congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent.
CCSS.Math.Content.HSG-CO.B.8 Explain how the criteria for
triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
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