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Congruent Figures
• Already know:
– Same size, same shape
– Congruent segments (same length)
– Congruent angles (same measure)
• Congruent triangles (and polygons)
– Mentally:
Can slide/rotate/flip one shape onto the other
– Definition:
Can match up vertices, sides, and angles
so that corresponding parts are congruent.
• Congruent triangles
ABC  DEF
Write:
• Then: A
D, B
E, C
F
ACB  DFE
• Order is important!
• Corresponding Parts
ABC  DEF
implies:
AB  DE
BC  EF
AC  DF
A   D
B   E
C  F
Corresponding Parts of Congruent Triangles are Congruent
(CPCTC)
mD
TC
GO
GDO
A
ACT
Z  J , A  O, K  E
ZA  JO, AK  OE , ZK  JE
NEV
AV
RV
N
mE
VNE
Isosceles Triangles
• Already know:
– Two sides are congruent
• Isosceles Triangle Theorem (ITT)
– If two sides of a triangle are congruent,
then the angles opposite them are
congruent.
• Converse of Isosceles Triangle Theorem
(Converse of ITT)
– If two angles of a triangle are congruent, then
the sides opposite them are congruent.
Equilateral Triangles
• Already know:
– All three sides are congruent
• ITT tells us:
– Opposite angles are congruent
– So...
Equilateral triangles are equiangular
(and have 60 degree angles)
– And…
Equiangular triangles are equilateral
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