Transcript 4.2 Congruence and Triangles

4.2 Congruence and Triangles
• Two geometric figures are
congruent if they have exactly the
same size and shape.
• When two figures are
congruentcorresponding angles
are congruent and corresponding
sides are congruent.
ABC =̃
PQR
B
Q
A
C
P
R
mA  mP
AB  PQ
mB  mQ
mC  mR
BC  QR
CA  RP
Third Angles Theorem
• If two angles of one triangle are congruent
to two angles of another triangle, then the
third angles are also congruent.
Properties of Congruent
Triangles
• Reflexive Property: Every triangle is
congruent to itself.
• Symmetric Property of Congruent
Triangles: If ABC =̃ DEF, then
DEF =̃ ABC
• Transitive Property of Congruent
Triangles:
If ABC =̃ DEF and DEF =̃ JKL,
then ABC =̃ JKL.
Practice Problems
• Name the congruent figures
E
B
D
A
ABC=̃
EFD
C
F
• Given M =̃ G and N =̃ H, find the
value of x.
H
M
142°
N
J
P
G
X=32
More Practice Problems
Given that N =̃ R and L =̃ S, find the
value of x.
M
R
N
55°
65°
L
S
(2X+30)°
T
X=15
Given that
LMN =̃
answer the following:
PQR,
P
N
Q
45°
R
L
mP= 105°
mM= 45°
mR= 30°
mN= 30°
105°
QR =̃ MN
LN =̃ PR
M
Identify any figures that can be
proved congruent. If congruent,
write a congruence statement.
A
B
C
D