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Unit 4
TRIANGLE FUN 
••I Ican
canuse
usethe
theangle
anglesum
sum
theorem
theorem
• I can the exterior angle
• I can the exterior angle
theorem
theorem
Learning Targets
Lesson 4-1
sum
angles
180°
30°
m∠1 = 28°
m∠1 = 120°
58° 32°
32°
m∠1 = 56°
m∠2 = 56°
m∠3 = 74°
58°
exterior
not
remote
interior
exterior
angle
sum
remote
interior angles
m∠1 = m∠A + m∠B
m∠1 = 115°
2x + 95 = 145
2x = 50
x = 25
140°
40°
75°
115°
65°
55°
55°
70°
125°
55°
95°
ASSIGNMENT:
4-1Worksheet
4.2 Congruent Triangles
Learning Target:
• I can name and label corresponding parts
of congruent triangles.
Instruction
Naming
Triangles
Triangles are
named by their
______________.
vertices
ABC
A
B
C
size
shape
Angle Measure
Betweenness
Collinearity
Distance
m∠A =m∠J AB = JK
m∠B = m∠K BC = KL
m∠C = m∠L AC = JL
ABC  JKL
Match up the letters in the same
“position” AND look at the ‘tick
marks’ in the picture! Match the
congruent pieces!
Warm Up
• I can recognize and use the
SSS, SAS, ASA, AAS, and HL
Postulates to see if triangles are
the same.
Lesson 4.3
CAN’T USE!!!
40
40
50
50
CAN’T USE!!!
6
40°
40°
SAS
∆DNV ≅ ∆BCX
SSS
∆TRS ≅ ∆SUT
HL
∆JKL ≅ ∆MNP
AAS
∆NJK ≅ ∆LMK
Your turn! Try e-h!
SAS
∆CDA ≅ ∆BDA
ASA
∆RST ≅ ∆UVT
AAS
∆RUT ≅ ∆RST
SAS
∆FJH ≅ ∆GHJ
A
M
R
W
G
MG ≅ AC
C
D
X
G
Y
Z
YZ ≅ DK
K
D
A
E
B
C
∠B ≅ ∠E
or ∠C ≅ ∠F
F
ASSIGNMENT:
“Swimming through triangles”
worksheet, both sides
(Pages 3 – 4)
Warm Up
PROOFS!
Lesson 4.4
Given
Given
TS ≅ TS
∆RST ≅ ∆UTS
Reflexive
SSS
Given
Given
∠RSU ≅ ∠TSU
US ≅ US
∆RSU ≅ ∆TSU
Def’n of angle bisector
Reflexive
SAS
Your Turn…
Given
Given
BD ≅ BD
∆ABD ≅ ∆CBD
∠A ≅ ∠C
Reflexive
SSS
CPCTC
Given
Given
DF ≅ DF
∠EDF ≅ ∠GFD
∆EDF ≅ ∆GFD
DG ≅ FE
Reflexive
AIA ≅↔ || lines
AAS
CPCTC
Given
Given
BC ≅ BC
∆BAC ≅ ∆BDC
∠A ≅ ∠D
Reflexive
HL
CPCTC
Your Turn…
BC || AD
BC ≅ AD
BD ≅ BD
∠CBD ≅ ∠ADB
∆ABD ≅ ∆CDB
Given
Given
Reflexive
AIA ≅↔ || lines
SAS
Your Turn…
∠D ≅ ∠F
GE bisects ∠DEF
GE ≅ GE
∠DEG ≅ ∠FEG
∆DEG ≅ ∆FEG
DE ≅ FE
Given
Given
Reflexive
Def. of angle bisector
AAS
CPCTC
Group Activity
Please put your tables into groups of 4
(push 2 tables together!)
We will rotate through 4 stations to fill out
proofs  You will have approximately 4
minutes per station. Work quickly but
accurately!
Warm Up
4.5 Isosceles and Equilateral
Triangles
Learning Targets
• I can use properties of isosceles triangles.
• I can use properties of equilateral
triangles.
Vertex angle
2 congruent
sides
opposite
2 congruent sides
Base angles
2 sides
opposite
congruent
congruent
FX ≅ OX
Small triangle: Use
3 letters to name
the angles!
∠SRT ≅ ∠STR
∠I ≅ ∠N
SV ≅ ST
40 + 2x + 2x = 180
40 + 4x = 180
4x = 140
x = 35
2x + 6 = 3x – 6
6=x–6
12 = x
L
2x + 1
3x – 2
N
M
2x + 1
= 3x – 2
1=x–2
5x – 2
x=3
equiangular
60
6x = 60
x = 10
6x – 5 = 5x
– 5 = -1x
5 =x
F
2x – 2
2x – 2
x+5
= x+5
x–2=5
x=7
H
3x – 9
G
Isosceles 
So base angles are congruent!
CD ≅ CG
DE ≅ GF
∠CDE ≅ ∠CGF
∆CDE ≅ ∆CGF
CE ≅ CF
Given
Given
ITT
SAS
CPCTC
Warm Up
4.6 Constructing Triangles
Use the construction instructions to work
through the constructions at your table.
Please raise your hand if you need
assistance!