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Bell Work
• A regular hexagon has a total perimeter of 120 inches.
Find the measure of each side of the polygon.
A hexagon has 6 sides. Since
it’s a regular hexagon all of the
sides are equal in length.
120 ÷ 6 = 20 inches
Each side measures 20 inches.
Identifying congruent figures
• Two geometric figures are congruent if they have
exactly the same size and shape.
NOT CONGRUENT
CONGRUENT
Congruency
• When two figures are congruent, there is a
correspondence between their angles and sides such
that corresponding angles are congruent and
corresponding sides are congruent.
• What does congruent mean? Congruent means that they
are the same or equal
• What does the symbol look like?
≅
Triangles
Corresponding angles
A ≅ P
B ≅ Q
C ≅ R
Corresponding Sides
AB ≅ PQ
BC ≅ QR
CA ≅ RP
B
A
Q
CP
R
How do you write a congruence statement?
• There is more than one way to write a congruence
statement, but it is important to list the corresponding
angles in the same order. Normally you would write
∆ABC ≅ ∆PQR, but you can also write that ∆BCA ≅
∆QRP
Ex. 1 Naming congruent parts
• Write a congruence statement.
∆DEF ≅ ∆RST
• Identify all parts of congruent
corresponding parts.
F
R
E
S
• Angles: D≅ R, E ≅ S, F ≅T
• Sides DE ≅ RS, EF ≅ ST, FD ≅ TR
D
T
Third Angle Theorem
• If any two angles of one triangle are congruent to two
angles of another triangle, then the third angles are
also congruent to one another.
• If A ≅ D and B ≅ E, then C ≅ F.
B
Why does that work?
C
A
E
D
F
Ex. 3 Try this challenge!
• In the diagram, N ≅ R and L ≅ S.
From the Third Angles Theorem, you
know that M ≅ T. So mM = mT.
• Find the value of x.
M
(2x + 30)° T
R
55°
N
65°
L
S
• From the Triangle Sum Theorem,
mM=180° - 55° - 65° = 60°
• mM = mT
(2x + 30)° = 60°
2x = 30
x = 15
Ex. 2
• In the diagram NPLM ≅ EFGH
• Find the value of y
Hint: You know that N ≅ E.
So, mN = mE.
(7y + 9)° = 72°
7y = 63
y=9
F
M
8m
L
G
110°
(2x - 3) m
87°
P
(7y+9)°
72°
10 m
N
E
H
Practice