Name:_______________________________________________
Period ___________
Geometry Unit 4: Triangle Congruence
Part I: Definition of Congruent Triangles
1. Given ∆APV ≅ ∆GSL, write congruence statements for all the corresponding parts that are congruent.
S
S
Part II: Triangle Congruence: SSS, SAS, ASA, AAS, HL
G
List the method that justifies the triangles being congruent and write a congruence statement.
G
2.
4.
3.
5.
What other information is needed to prove the triangles congruent by the given method. Explain your answer.
6. HL
7. SAS
G
K
S
O
U
C
D
R
D
Part III: Proofs
Fill in the missing statements for the 2 column proofs below.
̅̅̅̅
̅̅̅̅ // 𝑄𝑃
8. Given: 𝐿𝑀
̅̅̅̅
𝐿𝑄 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ̅̅̅̅̅
𝑀𝑃
Prove: ∆𝐿𝑀𝑁 ≅ ∆𝑄𝑃𝑁
̅̅̅̅
9. Given: ̅̅̅̅
𝐴𝐸 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 𝐵𝐶
̅̅̅̅
̅̅̅̅
𝐴𝐵 // 𝐷𝐸
̅̅̅̅
Prove: 𝐴𝐶 ≅ ̅̅̅̅
𝐸𝐶
M
A
B
N
L
C
Q
D
E
P
Statements
Reasons
Statements
Reasons
1.
1. Given
1.
1. Given
2.
2. Given
2.
2. Given
3.
3. Definition of bisect
3.
3. Def. of seg. bisector
4.
4.Vertical ∠s ≅
4.
4. AIA ≅
5.
5. AIA ≅
5.
5. Def. of Vertical angles
6.
6. ASA
6.
6. AAS
7.
7. CPCTC
Part IV: Rigid Motions and Triangle Congruence
10. What postulate/theorem justifies the following
triangles congruent?
11. What postulate/theorem justifies the following
triangles congruent?
A
P
T
D
E
R
C
B
Q
F
U
S
What rigid motions justify the triangles being congruent?
What rigid motions justify the triangles being congruent?
Congruence Statement: ________________________
Congruence Statement: ________________________
Part V: Rigid Motions and Triangle Congruence in the Coordinate Plane
12. ∆WYZ and ∆WYX are shown in the coordinate plane.
Explain using transformations how ∆ABC ≅ ∆DEF.
______________________________________________________________
______________________________________________________________
Explain how you can use the transformation you said above to prove ∆ABC ≅ ∆DEF.
______________________________________________________________
______________________________________________________________
______________________________________________________________
13. Given X(5, 2), Y (1, 5), Z (0, 0), P(-3, 3), Q(-7, 6) and R(-8, 1), explain how ∆XYZ ≅ ∆PQR using triangle
congruence criteria.
What postulate/theorem justifies the triangles being congruent? ____________
14. Are ∆JKL and ∆J’’K’’L’’ congruent? ______
Explain the rigid motions that were used to create ∆J’’K’’L’’.
_____________________________________________________
_____________________________________________________
15. ∆THX has vertices T(1, 1), H(3, 4) and X(4, 0).
Translate ∆THX using the rule (x, y) →(x – 3, y + 2) to create ∆T’H’X’.
T’ __________
H’ __________ X’ __________
Rotate ∆T’H’X’ 180° to create ∆T’’H’’X’’.
T’’ __________
H’’ __________ X’’ __________
Write a motion rule to describe the rotation above:
_____________________________________________
Write one rule that would change ∆THX to ∆T’’H’’X’’ in one step.
___________________________________________
Part VI: Example Multiple Choice Questions:
17. Given: PQ bisects RQS and RPS
16. Select all the reason why the triangles could be
congruent:
R
A. SSS
B. SAS
C. AAS
D. ASA
E. HL
Q
P
S
Part 1: What additional information could be used to show
that the triangles are congruent?
A. R  S Definition of bisect
B. RQ  SQ Definition of bisect
C. PQ  PQ The symmetric property of equality
D. PQ  PQ The reflexive property of equality
Part 2: Which congruence postulate is used to show that
the triangles are congruent.
A. AAS
B. SAS
C. ASA
D. There is not enough information
19. Which of the following would not be needed to prove
A
that the triangles are congruent.
H
18. Select all that would need to be true to show the
X
triangles are congruent by SAS.
A. XY  WY
B. XZY  WZY
C. X  W
D. YZ  YZ
E. XYZ  WYZ
Given: MA  HS; A  H
Y
Z
W
20. Given ΔPQR  ΔXYZ which of the following must be
true:
A. Any transofrmation will map ΔPQR onto ΔXYZ
B. Only a reflection will map ΔPQR onto ΔXYZ
C. R will be congruent to Y
D. PR will be congruent to XZ
A. M  S
B. T is the midpoint of MS
C. ATM  HTS
M
T
S
D. AT  HT
21. ΔABC is reflected over the x-axis and the reflected
over the y-axis to create ΔA’’B’’C’’. Select all that apply:
A. ΔA”B”C” is a 90° counterclockwise rotation of ΔABC
B. ΔA”B”C” is a 180° rotation of ΔABC
C. ΔA”B”C” is not congruent to ΔABC
D. ΔA”B”C” is congruent to ΔABC