4.3
Congruent Triangles
We will…
…name and label corresponding parts of
congruent triangles.
…identify congruence transformations.
Corresponding parts
of congruent triangles
Triangles that are the same size and shape
are congruent triangles.
Each triangle has three angles and three
sides. If all six corresponding parts are
congruent, then the triangles are
congruent.
Corresponding parts
of congruent triangles
Y
B
Z
C
A
X
If ΔABC is congruent to ΔXYZ , then vertices of the two triangles
correspond in the same order as the letter naming the triangles.
ΔABC ~
= ΔXYZ
Corresponding parts
of congruent triangles
Y
B
Z
C
A
X
ΔABC ~
= ΔXYZ
This correspondence of vertices can be used to name the
corresponding congruent sides and angles of the two triangles.
Definition of Congruent
Triangles (CPCTC)
Two triangles are congruent if and
only if their corresponding parts
are congruent.
CPCTC
Corresponding Parts of Congruent
Triangles are Congruent
ARCHITECTURE A tower roof is composed of
congruent triangles all converging
toward a point at the top. Name the
corresponding congruent angles
and sides of HIJ and LIK.
Answer: Since corresponding parts of congruent triangles
are congruent,
The support beams on the fence form congruent
triangles.
a. Name the corresponding
congruent angles and sides of
ABC and DEF.
Answer:
b. Name the congruent triangles.
Answer: ABC DEF
Properties of Triangle
Congruence
Congruence of triangles is reflexive,
symmetric, and transitive.
REFLEXIVE
K
K
L
J
ΔJKL ~
= ΔJKL
L
J
Properties of Triangle
Congruence
Congruence of triangles is reflexive,
symmetric, and transitive.
SYMMETRIC
K
L
J
~
If ΔJKL = ΔPQR,
then ΔPQR ~
= ΔJKL.
Q
R
P
Properties of Triangle
Congruence
Congruence of triangles is reflexive,
symmetric, and transitive.
TRANSITIVE
K
L
~
If ΔJKL = ΔPQR, and
ΔPQR ~= ΔXYZ, then
~ ΔXYZ.
ΔJKL =
J
Y
R
P
Z
X
Q
IDENTIFY CONGRUENCE
TRANSFORMATIONS
If you slide ΔABC down and to the
right, it is still congruent to ΔDEF.
B
E
C
F
A
D
B
C
A
IDENTIFY CONGRUENCE
TRANSFORMATIONS
If you turn ΔABC,
it is still congruent to ΔDEF.
A
B
C
A
B
C
E
F
D
IDENTIFY CONGRUENCE
TRANSFORMATIONS
If you flip ΔABC,
it is still congruent to ΔDEF.
B
C
A
E
A
C
F
B
D
COORDINATE GEOMETRY The vertices of RST are
R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST
are R(3, 0), S(0, ─5), and T(─1, ─1). Verify that
RST RST.
Use the Distance Formula to find the length of each side of
the triangles.
Use the Distance Formula to find the length of each side of
the triangles.
Use the Distance Formula to find the length of each side of
the triangles.
Answer: The lengths of the corresponding sides of two
triangles are equal. Therefore, by the definition
of congruence,
Use a protractor to measure the angles of the triangles. You
will find that the measures are the same.
In conclusion, because
,
COORDINATE GEOMETRY The vertices of RST are
R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST 
are R(3, 0), S(0, ─5), and T(─1, ─1). Name the
congruence transformation for RST and RST.
Answer: RST is a
turn of RST.
COORDINATE GEOMETRY The vertices of ABC are
A(–5, 5), B(0, 3), and C(–4, 1). The vertices of ABC
are A(5, –5), B(0, –3), and C(4, –1).
a. Verify that ABC ABC.
Answer:
Use a protractor to verify that
corresponding angles are
congruent.
b. Name the congruence transformation for ABC
and ABC.
Answer: turn
BOOKWORK:
p. 195
#9 – 19,
#22 – 25 (just name the congruence transformation)
HOMEWORK:
p.198
Practice Quiz