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Chapter 3.5
3.5 Congruence & Triangles
Identifying Congruent Figures
- Two Geometric figures are congruent if they have exactly the same size and shape.
-
When two figures are congruent, there is a correspondence between their angles and
sides.
o It is written that ABC  PQR b/c
Corresponding Angles
Corresponding Sides
Mapping
M  K
MI  KE
MK
I  E
IC  EY
IE
C  Y
MC  KY
CY
M
K
Training Time #1
 The  triangles represent the triangles in the picture.
Write a congruence statement. Write all pairs of
congruent corresponding parts. (List all the congruent
angles and the congruent sides)
Space Provided to Work:
C
E
R
Y
I
T
K
S
T
3rd Angles Theorem
 If two angles of one triangle are congruent to two
angles of another triangle, then the third angles are also
congruent.
 U  E & T  T’, as a result the 3rd angles will
be congruent G  R.
I
E
T'
U
E
G
 2003 McDougal Littell &  2008 Geometer’s Sketchpad; Adapted by Paul Cestaric
R
Chapter 3.5
M
E
P
Training Time #2
 Find the value of x.
55
(2x + 30)
65
K
A
U
Space Provided to Work:
T
Training Time #3
 Decide whether
the triangles are
congruent. Justify
your reasoning.
10 cm
P
12 cm
6 cm
92
L
12 cm
U
10 cm
PL
TO
Space Provided to Work:
 2003 McDougal Littell &  2008 Geometer’s Sketchpad; Adapted by Paul Cestaric
6 cm
O
Chapter 3.5
B
A
Training Time #4
The diagram represents the
triangular stamps shown in
the photo. Prove that
AEB  DEC;
E
C
D
Given: AB DC, AB  DC, & E is
the midpoint of BC & AD
Space Provided to Work:


Symmetric Property of Congruent
Triangles
o If ABC  DEF, then
DEF  ABC
B
C
Properties of Congruent Triangles
 Reflexive Property of Congruent
Triangles
o Every triangle is congruent to
itself.
F
A
L
K
D
Transitive Property of Congruent
Triangles
o If ABC  DEF and DEF
 JKL, then ABC  JKL.
J
 2003 McDougal Littell &  2008 Geometer’s Sketchpad; Adapted by Paul Cestaric
E
Chapter 3.5
3.5 Congruence & Triangles
Identifying Congruent Figures
- Two Geometric figures are _________________ if they have exactly the same ________
and _________.
- When two figures are ___________________, there is a correspondence between their
______________ and ____________.
I
o It is written that ABC  PQR b/c
Corresponding Angles
Corresponding Sides
Mapping
M  K
MI  KE
MK
I  E
IC  EY
IE
C  Y
MC  KY
CY
M
K
Training Time #1
 The  triangles represent the triangles in the picture.
Write a congruence statement. Write all pairs of
congruent corresponding parts. (List all the congruent
angles and the congruent sides)
Space Provided to Work:
R
Y
I
T
K
S
T
3rd Angles Theorem
 If ______ angles of one triangle are ______________
to ______ angles of another triangle, then the ________
angles are also congruent.
 U  E & T  T’, as a result the 3rd angles will
be congruent G  R.
C
E
E
T'
U
E
G
 2003 McDougal Littell &  2008 Geometer’s Sketchpad; Adapted by Paul Cestaric
R
Chapter 3.5
M
E
P
Training Time #2
 Find the value of x.
55
(2x + 30)
65
K
A
U
Space Provided to Work:
T
Training Time #3
 Decide whether
the triangles are
congruent. Justify
your reasoning.
10 cm
P
12 cm
6 cm
92
L
12 cm
U
10 cm
PL
TO
Space Provided to Work:
 2003 McDougal Littell &  2008 Geometer’s Sketchpad; Adapted by Paul Cestaric
6 cm
O
Chapter 3.5
B
A
Training Time #4
The diagram represents the
triangular stamps shown in
the photo. Prove that
AEB  DEC;
E
C
D
Given: AB DC, AB  DC, & E is
the midpoint of BC & AD
Space Provided to Work:


Symmetric Property of Congruent
Triangles
o If ABC  DEF, then
DEF  ABC
B
C
Properties of Congruent Triangles
 Reflexive Property of Congruent
Triangles
o Every triangle is congruent to
itself.
F
A
L
K
D
Transitive Property of Congruent
Triangles
o If ABC  DEF and DEF
 JKL, then ABC  JKL.
J
 2003 McDougal Littell &  2008 Geometer’s Sketchpad; Adapted by Paul Cestaric
E