Math 5270
Transformational Geometry
Day 7
Summer 13
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Math 5270 Transformational Geometry
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Journey continues
Day 7, Summer 13
Math 5270 Transformational Geometry
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Utah
Core description
of school
geometry
and- the
standards
Discuss with your table mates:
How does it compare with your understanding of school
geometry?
Do you have a sense of how their understanding develops
through the years?
Does our development so far helpful with seeing a progression?
What other things you think you might need to do in order to
successfully teach geometry as it is outlined in the core?
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Math 5270 Transformational Geometry
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Definition of congruence
Definition
Triangles 4ABC and 4A 0 B 0 C 0 are congruent if and only if there
is an isometry f : R2 → R2 such that f (A) = A 0 , f (B) = B 0 and
f (C ) = C 0 .
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Prove SSS
SSS
Triangles 4ABC and 4A 0 B 0 C 0 are congruent if and only if the
corresponding sides have equal lengths.
Let’s do this individually.
Write down what you think you need to prove.
If you’d like to check in with me or Tyler before proceeding.
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Math 5270 Transformational Geometry
5/12
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Prove
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SSS
Triangles 4ABC and 4A 0 B 0 C 0 are congruent if and only if the
corresponding sides have equal lengths.
Let’s do this individually.
Write down what you think you need to prove.
If you’d like to check in with me or Tyler before proceeding.
One person gives a big picture of the proof.
We pass the batton over throughout the proof.
Day 7, Summer 13
Math 5270 Transformational Geometry
5/12
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with a Trial Version of PDF Annotator - www.PDFAnno
Proof
of SAS
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Math 5270 Transformational Geometry
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Prove SAS
SAS
Triangles 4ABC and 4A 0 B 0 C 0 are congruent if and only if two
corresponding sides have equal lengths and the angles they
determine have equal measures.
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Math 5270 Transformational Geometry
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Proof of SAS
Day 7, Summer 13
Math 5270 Transformational Geometry
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Prove ASA
ASA
Triangles 4ABC and 4A 0 B 0 C 0 are congruent if and only if two
corresponding angles have equal measuers and the side they share
have equal lengths.
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Math 5270 Transformational Geometry
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Proof of ASA
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Math 5270 Transformational Geometry
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Questions?
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Math 5270 Transformational Geometry
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Homework
The rubric for scoring each homework prompt is as follows:
+4 Solution is mathematically valid, coherent, and elegantly
presented.
+3 Solution is correct, except for very minor errors in
computation or writing.
+2 Solution includes erroneous or extraneous work.
+1 Attempted but contains major errors or very hard to read and
understand.
+0 No attempt.
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Math 5270 Transformational Geometry
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