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Chapter 4- Triangle Congruence
Contributed by: DiLaura
4.1 
Classify the triangle by its angle measure.
obtuse triangle
 right triangle
equlangular triangle
acute triangle
4.1 
Classify the triangle by its angle measure.
obtuse triangle
 right triangle
equlangular triangle
acute triangle
86o
64o
4.1 
Classify the triangle by its side length.
isosceles triangle
scalene triangle
equilateral triangle
right triangle
4.1 
Classify the triangle by its side length.
equilateral triangle
 right triangle
scalene triangle
isosceles triangle
Find the 
measure of ∡A
4.2
m∡A = 
B
o
25o
C
127o
x
A
4.1
Find the 
measure of ∡A
m∡A = 
B
25o
o
x
A
C
4.1
Find the 
measure of ∡A
m∡A = 
A
o
x
51o
B
C
4.1
Given ∆ABC, find the 
value of x and
the length of side
AC
x = 
AC = 
A
2x + 7
4x - 3
B
3x - 5
C
4.2 
Given the following diagram of ∆CDB.  
Find the value of x
x = 
A
xo
o
B
52o
C
D
Given the following diagram of ∆CDB.  
Find the value of x
4.2 
x = 
C
xo
o
60o
D
B
112o
A
4.2 
Given the following diagram of ∆CDB.  
Find the value of x
x = 
A
xo
o
B
52o
C
D
Given the following diagram of ∆CDB.  Find the value of x.Then find the measureof the exterior angle.
4.2 
(2x + 16)o
A
x = 
C
m∡ACD = 
58o
D
B
(x + 12)o
o
4.3
Given that ∆FUN ≅ ∆TEA, identify the congruent corresponding parts.
∡N ≅ ∡
AT ≅ 
use capital letters for answers
4.3
Given that polygon MATH ≅ LOVE 
identify the congruent corresponding parts.
∡V ≅ ∡
AT ≅ 
use capital letters for answers
4.3
Given that ∆THE ≅ ∆SUP, and that UP = 2x + 12, and HE = 4x - 50.
Find the value of x
Find the length of UP
UP = 
x = 
4.3
Given that polygon PINK ≅ polygon BLUE,
how many pair of congruent parts are there?
6: 3 pairs of angles & 3 pairs of sides
4: 4 pairs of angles only
3: 3 pairs of sides only
8: 4 pairs of sides & 4 pairs of angles
Given that ∆TEA ≅ ∆CUP, find the value of x and y.
4.3
T
3x - 7
x = 
52o
E
A
U
P
y = 
11.9
y
C
Given that ∆HOP ≅ ∆RUF, and themeasure of ∡H = 32o  and the measure of ∡O = 77o.  

Find the measure of the following:
m∡P = 
m∡R = 
m∡U = 
o
o
o
4.4
Tell if and why the triangles are congruent.
Not congruent, not enough info
∡A ≅ ∡C, thus ∆'s are ≅ by SAS ∆≅ Thm.
BD ≅ BD, thus ∆'s are ≅, by SSS ∆≅ Thm.
 ∆'s are ≅ by the definition of ≅∆'s 
A
B
D
C
4.4
Tell if and why the triangles are congruent.
Not congruent, not enough info
AB ≅ AC, thus ∆'s are ≅ by SSS ∆≅ Thm.
BD ≅ BD, thus ∆'s are ≅, by SAS ∆≅ Thm.
 ∆'s are ≅ by the definition of ≅∆'s 
A
B
D
C
4.4
Tell what value x must be in order for the
two triangles to be congruent by SSS ∆≅ Thm.
6x - 4
B
x = 
A
C
4x + 7
D
4.4
Tell if and how the two triangles are congruent.
C
A
Not congruent, not enough info
AC ≅ED, thus ∆'s are ≅ by SSS ∆≅
 ∡ABC ≅EBD, thus ∆'s are ≅ by SAS ∆≅
B
D
E
4.5
Identify the postulate or theorem that 
proves the two triangles are congruent.
not congruent, not enough info
∡B≅∡D, thus ∆'s ≅ by AAA ∆≅ thm.
AC ≅ AC, thus ∆'s≅ by ASA ∆ ≅ thm.
AB ≅CD, thus ∆'s ≅ by AAS ∆ ≅ thm. 
A
B
D
C
4.5
What additional information do you need to know in order to prove ∆ABC ≅ ∆EBD by ASA?
 ∡BDE ≅ ∡BCA
∡A ≅ ∡C
 AC ≅ ED
∡B ≅ ∡B
A
D
B
E
C
4.5
Identify the postulate or theorem that 
proves the two triangles are congruent.
A
not congruent, not enough info
∆'s ≅ by AAA ∆≅ thm.
∆'s≅ by ASA ∆ ≅ thm.
∆'s ≅ by AAS ∆ ≅ thm.
B
E
D
C
4.5
Identify the postulate or theorem that 
proves the two triangles are congruent.
not congruent, not enough info
∆'s ≅ by HL ∆≅ thm.
AC ≅ AC, thus ∆'s≅ by ASA ∆ ≅ thm.
∆'s ≅ by SAS ∆ ≅ thm.
A
D
B
C
4.5
Identify the postulate or theorem that 
proves the two triangles are congruent.
A
not congruent, not enough info
∆'s ≅ by AAA ∆≅ thm.
∆'s≅ by SAS ∆ ≅ thm.
∆'s ≅ by ASA ∆ ≅ thm.
B
E
D
C
4.6
 False
 True; ∆'s ≅ by SAS, and AT ≅ UC by CPCTC
 True; ∆'s ≅ by ASA, and AT ≅ UC by def. ≅ sides
 True; ∆'s ≅ by SAS, and AT ≅ UC by SSS
Tell if the highlighted statementis true or false and why (if it's true).                  AT ≅ UC
T
A
E
P
U
C
4.6
 True; ∆'s ≅ by SAS, and ∡T ≅ ∡C by CPCTC
 True; ∆'s ≅ by SSS, and AT ≅ UC by SAS
 False
 True; ∆'s ≅ by SAS, and ∡T ≅ ∡C by Third ∡ Thm.
Tell if the highlighted statementis true or false and why (if it's true).                  ∡T ≅ ∡C
T
A
E
P
U
C
Tell if (and why) the highlighted statement is true.

∆'s ≅ by SSS, Thus true by CPCTC
∆'s ≅ by SSS, Thus false ∡'s ≇
 ∆'s  ≅ by SAS , Thus true by CPCTC
∆'s are not ≅, thus false ∡'s ≇
∡A ≅ ∡B
A
C
B
D
4.6
Match the theorem that proves the ∆'s are ≅
A. SSS     B. SAS    C. AAS    D. ASA     E. HL
∆'s ≅
Choose from:
use capital letters
∆'s ≅
∆'s ≅
4.8
A
C
Find the measure ∡A & ∡B
m∡A=
D
24o
m∡B=
76o
B
E
4.8
Find the measure ∡A & ∡DBC
m∡A=
m∡DBC=
A
D
45o
C
B
4.8
Find the measure ∡A & the value of x
m∡A=
x =
B
C
A
(7x - 3)o
4.8
Find the measure ∡A, the value of x, and
the length of AB
m∡A=
x =
AB =
(3x + 3)
B
C
(5x - 17)
A
Find the measure ∡B, the value of x, and
the length of CA
4.8
m∡B=
CA =
x =
(½x + 6)
B
(2x)
C
(2x)
A
4alg
Solve for x.
5
2
x  + 7 = 22
x =
4alg
Solve for x.
3
4
x  - 4 = 14
x =
4alg
Solve for x.
5
4
x  + 7 =
x =
3
2
x  + 3
4alg
Solve for x.
3x2  = x2 + 50
x =
4alg
Solve for x.
-2x2  = -3x2 + 144
x =
Find the missing angle measures for ∡1 & ∡2
m∡1 =
m∡2 =
37o
o
o
1
77o
2
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