G.CO.7 STUDENT NOTES & PRACTICE WS #7
1-
- geometrycommoncore.com
7
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.
CONCEPT
Use
Congruence of triangles is defined by:
Two triangles are congruent if and only if
one can be mapped onto the other by one or more rigid motions.
NWS (Now You Trv Some)
1. ln your own words explain how you know if two triangles are congruent or not.
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A congruence statement for triangles
relates one identical object to another by
identifying the corresponding parts that
match each other.
A uStN G oNE o{e
AABC = ADEF
lD
lB=lE
LA=
AB= DE
BC=EF
Pn
ZC=ZF
Corresponding Parts of Congruent Triangles are Congruent.
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NYIS (Now You Trv Somel
2. Determine the congruent sides and angles from the congruence statement.
b)APLC = AMNB
a) ATRY = AAXD
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Ll = LD
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Determine congruence using a single or sequence of isometric transformations.
A reflection (x, y)-Atranslation (x, y)--> (x+3,yArotation (x, y)---> (-y,x) maps
. these two triangles,
maps these two triangles,
maps these two triangles,
so AABC = ARGD
so AABC = AGHI
so AABC = ATKI
>(x,-y)
5)
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G.CO.7 STUDENT NOTES
& PRACfiICE WS #7
-
geometrycommoncore.com
Are AABC = AKJL? ls there a sequence of isometric transformations that map one onto the other?
A reflection over the y axis
A translation of
YES, AABC
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= AKJL is because I can map AABC onto AKJL using a reflection and then a translation.
N[I|S (Now You Trv Somel
3. Are AABC = ADEF
Determine a sequence of isometric transformation from AABC to ADEF (name it specifically and also graph it)
Original Relationship
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4. Name the transformation or sequence of transformations that map one figure onto the other. Then
complete the congruence statement.
Transformations: (Start with AABC)
A reflection over
the Y &rzt S
followed by
A translation of
^ABC
=
A DEF
Transformations: (Start with AABC )
A reflection over
the X kXt9
Followed by
A translation
AABC
=A
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