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Chapter 6 ● Assignments 105
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Assignment Assignment for Lesson 6.1
Name _____________________________________________ Date ____________________
Constructing Congruent Triangles or NotConstructing Triangles
In each exercise, do the following.
a. Use the given information to construct a triangle.
b. Determine whether it is possible to use the given information to construct another triangle that is not congruent to the first triangle.
c. If it is possible to construct another triangle that is not congruent to the first triangle, construct it. If it is not possible, explain why not.
1. Use the two line segments and the included angle to construct � X�Y�Z�.
X Y
Y Z
Y
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106 Chapter 6 ● Assignments
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2. Use the three angles to construct � J�K�L�.
J K L
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3. Use the two angles and the included side to construct � M�N�P�.
M
N
NM
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108 Chapter 6 ● Assignments
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Assignment Assignment for Lesson 6.2
Name _____________________________________________ Date ____________________
Congruence TheoremsSSS, SAS, ASA, and AAS
1. Complete the proof of the Angle-Side-Angle (ASA) Congruence Theorem.
Given: � A � �D, ___
AC � ___
DF , �C � �F
Prove: � ABC � � DEF
A
B
C
D
E
F
Statements Reasons
1. � A � �D, ___
AC � ___
DF , �C � �F 1.
2. � ABC � � DEF 2.
3. � A � , � �E, �C � 3. Definition of Similar Triangles
4. AB ___ DE
� BC ___ EF
� AC ___ DF
4.
5. AC � DF 5.
6. AC
___ DF
� 6. Division Property of Equality
7. AB ___ � ____ EF
� 1 7. Substitution
8. AB � DE, BC � EF 8.
9. 9. Definition of Congruence
10. � ABC � � DEF 10.
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2. Write a two-column proof of the Angle-Angle-Side (AAS) Congruence Theorem.
Given: � A � �D, �B � �E, ___
BC � ___
EF ,
Prove: � ABC � � DEF
A
B
C
D
E
F
Write a Given statement and state the theorem that proves the triangles are congruent. Then write a congruence statement.
3. A CB
E D
4. M A
H T
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6
Determine the information that is needed to use the indicated theorem to show that the triangles are congruent.
5. � FJG � �HJG by SAS 6. �V W X � � Z Y X by AAS
F
G
HJ
V
W
X
Y
Z
7. The figure shows a basic plan for a decorative porch roof. In the figure,
___
DP is perpendicular to ___
AG and ___
AP � ___
PG . Use a two-column proof to
show �DPA � �DPG.
A P G
D
B
C
F
E
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Assignment Assignment for Lesson 6.3
Name _____________________________________________ Date ____________________
Right Triangle Congruence Theorems HL, LL, HA, and LA
Write a Given statement and state the theorem that proves the triangles are congruent. Then write a congruence statement.
1.
D
G
FH
2.
BX T
K
M
Determine the information that is needed to use the indicated theorem to show that the triangles are congruent.
3. � RQW � � RPW by HL
R W
Q
P
4. � JNZ � � HNC by LA
J
Z
N
C
H
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5. In the following figure, triangle ABD is an isosceles triangle and ___
AC is perpendicular
to ___
BD . Use a two-column proof to show that �B � �D.
A
B DC
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Assignment Assignment for Lesson 6.4
Name _____________________________________________ Date ____________________
CPCTC Corresponding Parts of Congruent Triangles are Congruent
1. What is the width of the swimming pool? Explain how you got your answer.
84 ft
82 ft
82 ft
2. Marcel is painting the triangular section of a shuffleboard court shown in the figure.
He starts by putting 41 feet of tape around the outside of the triangle. He knows
that the base of the triangle is 16 feet and each base angle of the triangle measures
50 degrees. What is the length of each leg?
50° 50°
16 ft
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Calculate the measure of angle 1. Show your work.
3. 110°
1
4.
136°
1
5. Use a two-column proof to show that ___
LM bisects ___
DF .
Given: ___
LF � ____
DM , ___
DL � ___
MF
Prove: ___
LM bisects ___
DF
D
F
X
L
M
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Assignment Assignment for Lesson 6.5
Name _____________________________________________ Date ____________________
Isosceles Triangle Theorems Isosceles Triangle Base Theorem, Vertex Angle Theorem, Perpendicular Bisector Theorem, Altitude to Congruent Sides Theorem, and Angle Bisector to Congruent Sides Theorem
1. Use the Isosceles Triangle Perpendicular Bisector Theorem to make a statement
about isosceles �CYX.
C
Y
X
D
2. Use the Triangle Base Theorem to make a statement about isosceles �PBD.
PH
B
D
3. Use the Isosceles Triangle Angle Bisector to Congruent Sides Theorem to make
a statement about isosceles �KSF.
K S
F
G T
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Solve for x.
4.
(2x – 7)°
(4x + 1)°
B G
K
Q
5.
R
T
S
V
L
RT = 7x – 10
SV = 5x + 8
6.
Z DF
P
25 x 2 – 11
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Chapter 6 ● Assignments 119
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6
7. Use a flow chart proof to show that segment AY is
congruent to segment CZ.
Given: ___
AB � ___
CB , � ____
AXY � � ____
CXZ
Prove: ___
AY � ___
CZ A C
B
Y Z
X
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Assignment Assignment for Lesson 6.6
Name _____________________________________________ Date ____________________
Direct Proof vs. Indirect Proof Inverse, Contrapositive, Direct Proof, and Indirect Proof
1. Consider the conditional statement “If a quadrilateral is a rectangle, then it is
a parallelogram.”
a. Identify the hypothesis and the conclusion.
b. Is the conditional statement true? Explain.
c. Write the converse of the conditional statement. Is the converse true? Explain.
d. Write the inverse of the conditional statement. Is the inverse true? Explain.
e. Write the contrapositive of the conditional statement. Is the contrapositive
true? Explain.
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2. Consider the conditional statement “If a triangle is equilateral, then the triangle
is equiangular.”
a. Identify the hypothesis and the conclusion.
b. Is the conditional statement true? Explain.
c. Write the converse of the conditional statement. Is the converse true? Explain.
d. Write the inverse of the conditional statement. Is the inverse true? Explain.
e. Write the contrapositive of the conditional statement. Is the contrapositive
true? Explain.
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3. Use an indirect two-column proof to show that the complements of congruent
angles are congruent.
2 1
4 3
Given: m�1 � m�2, m�1 � m�3 � 90°, m�2 � m�4 � 90°
Prove: m�3 � m�4
4. Write an indirect paragraph proof to show that an isosceles triangle cannot have a
base angle that is a right angle.
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