# Chapter 5 Skills Practice

```Lesson 5.1 вЂѓ Skills Practice
Name
Date
We Like to Move It!
Translating, Rotating, and Reflecting Geometric Figures
Problem Set
Transform each given geometric figure on the coordinate plane as described.
1. Translate trapezoid ABCD 11 units to the right.
y
A
A9
B
8
B9
6
C
D
4
C9
2
D9
0
28 26 24 22
2
4
6
8
x
22
24
26
28
5
2. Translate triangle EFG 8 units up.
y
8
6
4
2
0
28 26 24 22
22
2
4
6
E
8
x
F
24
26
28
G
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3. Rotate rectangle HJKL 90В° counterclockwise about the origin.
y
8
H
J
L
K
6
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
4. Rotate triangle MNP 180В° counterclockwise about the origin.
y
8
6
5
4
2
0
22
2
4
26
514вЂѓ
8
x
N
24
28
6
M
P
28 26 24 22
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Lesson 5.1 вЂѓ Skills Practice
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Name
Date
5. Rotate trapezoid QRST 90В° counterclockwise about the origin.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
R
24
S
26
28
Q
T
6. Rotate parallelogram WXYZ 180В° counterclockwise about the origin.
y
X
8
5
Y
6
4
W
2
Z
0
28 26 24 22
2
4
6
8
x
22
24
26
28
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7. Reflect triangle ABC over the y-axis.
y
B
8
A
6
4
2
C
0
28 26 24 22
2
4
6
8
2
4
6
8
x
22
24
26
28
8. Reflect parallelogram DEFG over the x-axis.
y
8
6
5
4
2
0
28 26 24 22
x
22
D
F
G
24
26
28
516вЂѓ
E
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Lesson 5.1 вЂѓ Skills Practice
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Name
Date
9. Reflect trapezoid HJKL over the x-axis.
y
J
K
8
6
4
H
2
0
28 26 24 22
L
2
4
6
x
8
22
24
26
28
10. Reflect quadrilateral MNPQ over the y-axis.
y
5
8
6
4
2
0
28 26 24 22
22
2
4
6
N
x
8
P
24
26
28
M
Q
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Determine the coordinates of each translated image without graphing.
11. The vertices of triangle ABC are A (5, 3), B (2, 8), and C (24, 5). Translate the triangle 6 units to the
left to form triangle AоЂ№ BоЂ№ CоЂ№.
The vertices of triangle AоЂ№ BоЂ№ CоЂ№ are AоЂ№ (21, 3), BоЂ№ (24, 8), and CоЂ№ (210, 5).
12. The vertices of rectangle DEFG are D (27, 1), E (27, 8), F (1, 8), and G (1, 1). Translate the rectangle
10 units down to form rectangle DоЂ№ EоЂ№ FоЂ№ GоЂ№.
13. The vertices of parallelogram HJKL are H (2, 26), J (3, 21), K (7, 21), and L (6, 26). Translate the
parallelogram 7 units up to form parallelogram HоЂ№ JоЂ№ KоЂ№ LоЂ№.
14. The vertices of trapezoid MNPQ are M (26, 25), N (0, 25), P (21, 2), and Q (24, 2). Translate the
trapezoid 4 units to the right to form trapezoid MоЂ№ NоЂ№ PоЂ№ QоЂ№.
15. The vertices of triangle RST are R (0, 3), S (2, 7), and T (3, 21). Translate the triangle 5 units to the left
and 3 units up to form triangle RоЂ№ SоЂ№ TоЂ№.
5
16. The vertices of quadrilateral WXYZ are W (210, 8), X (22, 21), Y (0, 0), and Z (3, 7). Translate the
quadrilateral 5 units to the right and 8 units down to form quadrilateral WоЂ№ XоЂ№ YоЂ№ ZоЂ№.
17. The vertices of triangle ABC are A (5, 3), B (2, 8), and C (24, 5). Rotate the triangle about the origin
90В° counterclockwise to form triangle AоЂ№ BоЂ№ CоЂ№.
The vertices of triangle AоЂ№ BоЂ№ CоЂ№ are AоЂ№ (23, 5), BоЂ№ (28, 2), and CоЂ№ (25, 24).
18. The vertices of rectangle DEFG are D (27, 1), E (27, 8), F (1, 8), and G (1, 1). Rotate the rectangle
about the origin 180В° counterclockwise to form rectangle DоЂ№ EоЂ№ FоЂ№ GоЂ№.
518вЂѓ
Determine the coordinates of each rotated image without graphing.
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Lesson 5.1 вЂѓ Skills Practice
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Name
Date
19. The vertices of parallelogram HJKL are H (2, 26), J (3, 21), K (7, 21), and L (6, 26). Rotate the
parallelogram about the origin 90В° counterclockwise to form parallelogram HоЂ№ JоЂ№ KоЂ№ LоЂ№.
20. The vertices of trapezoid MNPQ are M (26, 25), N (0, 25), P (21, 2), and Q (24, 2). Rotate the
trapezoid about the origin 180В° counterclockwise to form trapezoid MоЂ№ NоЂ№ PоЂ№ QоЂ№.
21. The vertices of triangle RST are R (0, 3), S (2, 7), and T (3, 21). Rotate the triangle about the origin
90В° counterclockwise to form triangle RоЂ№ SоЂ№ TоЂ№.
22. The vertices of quadrilateral WXYZ are W (210, 8), X (22, 21), Y (0, 0), and Z (3, 7). Rotate the
Determine the coordinates of each reflected image without graphing.
23. The vertices of triangle ABC are A (5, 3), B (2, 8), and C (24, 5). Reflect the triangle over the x-axis
to form triangle AоЂ№ BоЂ№ CоЂ№.
The vertices of triangle AоЂ№ BоЂ№ CоЂ№ are AоЂ№ (5, 23), BоЂ№ (2, 28), and CоЂ№ (24, 25).
5
24. The vertices of rectangle DEFG are D (27, 1), E (27, 8), F (1, 8), and G (1, 1). Reflect the rectangle
over the y-axis to form rectangle DоЂ№ EоЂ№ FоЂ№ GоЂ№.
25. The vertices of parallelogram HJKL are H (2, 26), J (3, 21), K (7, 21), and L (6, 26). Reflect the
parallelogram over the x-axis to form parallelogram HоЂ№ JоЂ№ KоЂ№ LоЂ№.
26. The vertices of trapezoid MNPQ are M (26, 25), N (0, 25), P (21, 2), and Q (24, 2). Reflect the
trapezoid over the y-axis to form trapezoid MоЂ№ NоЂ№ PоЂ№ QоЂ№.
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27. The vertices of triangle RST are R (0, 3), S (2, 7), and T (3, 21). Reflect the triangle over the x-axis to
form triangle RоЂ№ SоЂ№ TоЂ№.
28. The vertices of quadrilateral WXYZ are W (210, 8), X (22, 21), Y (0, 0), and Z (3, 7). Reflect the
5
520вЂѓ
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Lesson 5.2 вЂѓ Skills Practice
Name
Date
Hey, HavenвЂ™t I Seen You Before?
Congruent Triangles
Problem Set
Identify the transformation used to create nXYZ on each coordinate plane. Identify the congruent angles
and the congruent sides. Then, write a triangle congruence statement.
1.
Triangle BCA was reflected over the x-axis to
create triangle XYZ.
y
8
___ ___ ___
A
4
B
2
0
28 26 24 22
C
2
22
___ ___
BC > XYвЂЇ
вЂ‹ вЂЇ
вЂ‹, CAвЂЇвЂ‹
вЂ‹ вЂЇ> YZвЂЇвЂ‹
вЂ‹ вЂЇ
, and BAвЂЇвЂ‹
вЂ‹ вЂЇ> XZвЂЇвЂ‹
вЂ‹ вЂЇ
; /B > /X,
/CВ > /Y, and /A > /Z.
6
4
6
X
8
nBCA > nXYZ
x
Y
24
26
Z
28
2.
5
y
X
8
6
4
Z
Y
2
0
28 26 24 22
22
2
4
6
8
x
D
24
26
28
E
F
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y
P
8
6
4
2
28 26 24 22
Z
X
M
0
2
T
4
6
8
x
22
24
26
28
Y
4.
y
8
B
D
X
6
Z
4
5
N
2
Y
0
28 26 24 22
2
4
6
8
x
22
24
28
522вЂѓ
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Lesson 5.2 вЂѓ Skills Practice
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Name
Date
5.
y
Y
8
6
X
4
Z
2
0
28 26 24 22
F
2
4
6
x
8
22
24
A
26
28
W
6.
y
8
Z
6
4
X
2
0
28 26 24 22
2
22
24
5
Y
4
6
8
x
Q
M
26
28
R
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Lesson 5.2 вЂѓ Skills Practice
7.
page 4
y
Y
8
Z
N
6
4
R
2 G
X
28 26 24 22
0
2
4
6
8
2
4
6
8
x
22
24
26
28
8.
y
8
Y
6
4
5
X
Z
2
0
28 26 24 22
22
x
W
24
H
28
524вЂѓ
F
26
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Lesson 5.2 вЂѓ Skills Practice
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Name
Date
9.
y
T
Y
A
8
Z
6
4
V
2
X
0
28 26 24 22
2
4
6
x
8
22
24
26
28
10.
y
M
8
6
5
4
G
2
28 26 24 22
Y
X
B
0
2
4
6
8
x
22
24
26
28
Z
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Lesson 5.2 вЂѓ Skills Practice
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List the corresponding sides and angles, using congruence symbols, for each pair of triangles
represented by the given congruence statement.
11. nJPM > nTRW
___ ___ ____ ____
___ ____
JPвЂЇвЂ‹
вЂ‹ вЂЇ
, PMвЂЇвЂ‹
вЂ‹ вЂЇ> RWвЂЇвЂ‹
вЂ‹ вЂЇ
, and JMвЂЇвЂ‹
вЂ‹ вЂЇ> TWвЂЇвЂ‹
вЂ‹ вЂЇ
; /J > /T, /P > /R, and /M > /W.
вЂ‹ вЂЇ> TRвЂЇвЂ‹
12. nAEU > nBCD
13. nLUV > nMTH
14. nRWB > nVCQ
15. nTOM > nBEN
16. nJKL > nRST
17. nCAT > nSUP
18. nTOP > nGUN
526вЂѓ
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Lesson 5.3 вЂѓ Skills Practice
Name
Date
Side-Side-Side Congruence Theorem
Vocabulary
Define the term in your own words.
1. Side-Side-Side (SSS) Congruence Theorem
Problem Set
Determine whether each pair of given triangles are congruent by SSS. Use the Distance Formula and
a protractor when necessary.
1.
AB 5 DE 5 3
y
AC 5 DF 5 7
8
B
___________________
6
вЂ‡ вЂ‰вЂ‰d 5 в€љ
вЂ‹ вЂ‹вЂ‹(вЂЇx2 2 x1вЂЇ)2вЂ‹вЂ‹ вЂ‹1 (вЂ‹вЂ‹вЂЇy2вЂЇвЂЇ
2 y1вЂЇ)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
4
BC 5 вЂ‹в€љ(вЂ‹вЂ‹вЂЇ9 2 2вЂЇ)2вЂ‹вЂ‹ вЂ‹1 (вЂ‹вЂ‹вЂЇ4 вЂЇвЂЇ
2 7вЂЇ)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
_________________
A
C
__________
BC 5 в€љ
вЂ‹ вЂ‹72вЂ‹ вЂ‹1 (2вЂ‹3)вЂ‹2вЂ‹вЂЇвЂ‹вЂЇ
2
0
28 26 24 22
22
F
2
4
6
8
D
24
26
28
x
_______
BC 5 в€љ
вЂ‹ 49 1 9вЂЇвЂ‹вЂЇ
5
___
BC 5 вЂ‹в€љ58вЂЇвЂ‹вЂЇ< 7.62
___________________
E
вЂ‡ вЂ‰вЂ‰d 5 вЂ‹в€љвЂ‹вЂ‹(вЂЇx2 2 x1вЂЇ)2вЂ‹вЂ‹ вЂ‹1 (вЂ‹вЂ‹вЂЇy2вЂЇвЂЇ
2 y1вЂЇ)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
______________________
вЂ‰вЂ‰EF 5 вЂ‹в€љвЂ‹вЂ‹(вЂЇ1 2 8вЂЇ)вЂ‹вЂ‹2вЂ‹1 (вЂЇвЂ‹вЂ‹вЂЇвЂЇвЂЇ
23 2 (26)вЂЇ)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
__________
вЂ‰вЂ‰EF 5 в€љ
вЂ‹ вЂ‹вЂ‹(вЂЇ27вЂЇ)2вЂ‹вЂ‹ вЂ‹1 вЂ‹32вЂ‹ вЂ‹вЂЇвЂ‹вЂЇ
_______
вЂ‰вЂ‰EF 5 в€љ
вЂ‹ 49 1 9вЂЇвЂ‹вЂЇ
___
вЂ‰вЂ‰EF 5 вЂ‹в€љ58вЂЇвЂ‹вЂЇ< 7.62
BC 5 EF
The triangles are congruent by the
SSS Congruence Theorem.
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2.
page 2
y
J
8
6
4
G
H
2
0
28 26 24 22
2
22
L
4
6
x
8
K
24
26
28
M
5
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Name
Date
3.
y
B
8
6
4
R
G
2
0
28 26 24 22
2
4
6
8
x
22
D
M
24
26
28
A
5
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4.
page 4
y
8
P
6
4
M
N
2
0
28 26 24 22
Y
2
22
4
6
8
x
X
24
26
Z
28
5
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Name
Date
5.
y
C
W
8
M
6
4
2
0
28 26 24 22
2
4
6
8
x
22
Q
24
P
26
S
28
5
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Lesson 5.3 вЂѓ Skills Practice
6.
page 6
y
8
N
6
P
4
2
Q
0
28 26 24 22
2
4
6
8
x
22
T
24
26
R
S
28
5
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Lesson 5.3 вЂѓ Skills Practice
page 7
Name
Date
Perform the transformation described on each given triangle. Then, verify that the triangles are congruent
by SSS. Use the Distance Formula and a protractor when necessary.
7. Reflect nABC over the y-axis to form nXYZ. Verify that nABC > nXYZ by SSS.
вЂ‰вЂ‰AB 5 XY 5 12
y
вЂ‰вЂ‰BC 5 YZ 5 5
8
A
___________________
X
6
вЂ‡вЂЉвЂ‰вЂ‰вЂ‰d 5 в€љ
вЂ‹ вЂ‹вЂ‹(вЂЇx2 2 x1вЂЇ)2вЂ‹вЂ‹ вЂ‹1 вЂ‹вЂ‹(вЂЇy2вЂЇвЂЇ
2 y1вЂЇ)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
_______________________
4
вЂ‰вЂ‰AC 5 в€љ
вЂ‹ вЂ‹вЂ‹(вЂЇ24 2 (29)вЂЇ)вЂЇвЂЇвЂЇ
вЂ‹вЂ‹2вЂ‹1 (вЂ‹вЂ‹вЂЇ26 2 6вЂЇ)вЂ‹вЂ‹2вЂ‹вЂЇвЂ‹
2
)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
вЂ‰вЂ‰AC 5 в€љ
вЂ‹ вЂ‹52вЂ‹ вЂ‹1 вЂ‹вЂ‹(вЂЇ212вЂЇ
вЂЇвЂЇ
___________
0
28 26 24 22
2
4
6
x
8
_________
вЂ‰вЂ‰AC 5 в€љ
вЂ‹ 25 1 144вЂЇвЂ‹вЂЇ
____
22
вЂ‰вЂ‰AC 5 вЂ‹в€љ 169вЂЇвЂ‹вЂЇ5 13
24
___________________
B
C
26
28
Z
Y
вЂ‡вЂ‰вЂ‰вЂ‰d 5 вЂ‹в€љвЂ‹вЂ‹(вЂЇx2 2 x1вЂЇ)вЂ‹вЂ‹2вЂ‹1 (вЂ‹вЂ‹вЂЇy2вЂЇвЂЇ
2 y1вЂЇ)вЂ‹вЂ‹2вЂ‹вЂЇвЂ‹
___________________
вЂЉвЂЉвЂ‰XZ 5 вЂ‹в€љвЂ‹вЂ‹(вЂЇ4 2 9вЂЇ)2вЂ‹вЂ‹ вЂ‹1 вЂ‹вЂ‹(вЂЇ26вЂЇвЂЇ
2 6вЂЇ)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
______________
)2вЂ‹вЂ‹ вЂ‹вЂЇвЂ‹
вЂЉвЂЉвЂ‰XZ 5 вЂ‹в€љвЂ‹вЂ‹(вЂЇ25вЂЇ)2вЂ‹вЂ‹ вЂ‹1 вЂ‹вЂ‹(вЂЇ212вЂЇ
вЂЇвЂЇ
_________
вЂЉвЂЉвЂ‰XZ 5 вЂ‹в€љ25 1 144вЂЇвЂ‹вЂЇ
____
вЂЉвЂЉвЂ‰XZ 5 вЂ‹в€љ169вЂЇвЂ‹вЂЇ5 13
вЂ‰AC 5 XZ
5
The triangles are congruent by the
SSS Congruence Theorem.
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Lesson 5.3 вЂѓ Skills Practice
page 8
8. Rotate nDEF 180В° clockwise about the origin to form nQRS. Verify that nDEF > nQRS by SSS.
y
8
D
6
4
E
F
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
5
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Lesson 5.3 вЂѓ Skills Practice
page 9
Name
Date
9. Reflect nJKL over the x-axis to form nMNP. Verify that nJKL > nMNP by SSS.
y
8
6
4
2
0
28 26 24 22
2
4
6
x
8
22
24
J
K
26
28
L
5
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Lesson 5.3 вЂѓ Skills Practice
page 10
10. Translate nHMZ 10 units to the left and 1 unit down to form nBNY. Verify that nHMZ > nBNY
by SSS.
y
8
6
M
4
H
2
0
28 26 24 22
2
4
6
8
x
22
24
26
Z
28
5
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Lesson 5.3 вЂѓ Skills Practice
page 11
Name
Date
11. Rotate nAFP 90В° counterclockwise about the origin to form nDHW. Verify that nAFP > nDHW
by SSS.
y
A
8
6
4
P
2
F
0
28 26 24 22
2
4
6
8
x
22
24
26
28
5
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Lesson 5.3 вЂѓ Skills Practice
page 12
12. Translate nACE 3 units to the right and 9 units up to form nJKQ. Verify that nACE > nJKQ by SSS.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
A
24
26
C
28
E
5
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Lesson 5.4 вЂѓ Skills Practice
Name
Date
Make Sure the Angle Is Included
Side-Angle-Side Congruence Theorem
Vocabulary
Describe how to prove the given triangles are congruent. Use the Side-Angle-Side Congruence Theorem
1.
y
A
8
6
C
B
4
2
0
28 26 24 22
22
2
4
X
6
8
x
Z
24
26
28
Y
5
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Lesson 5.4 вЂѓ Skills Practice
page 2
Problem Set
Determine whether each pair of given triangles are congruent by SAS. Use the Distance Formula and a
protractor whenВ necessary.
1. Determine whether nABC is congruent to nDEF by SAS.
AB 5 DE 5 5
y
BC 5 EF 5 7
m/B 5 m/E 5 90В°
The triangles are congruent by the SAS
Congruence Theorem.
A
8
6
4
B
2
28 26 24 22
F
0
2
C
4
6
8
x
22
24
26
28
E
D
2. Determine whether nCKY is congruent to nDLZ by SAS.
y
C
8
5
L
Z
6
4
2
2
4
6
22
Y
K
24
26
28
540вЂѓ
D
8
x
0
28 26 24 22
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Lesson 5.4 вЂѓ Skills Practice
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Name
Date
3. Determine whether nFMR is congruent to nJQW by SAS.
y
8
M
6
F
4
W
2
0
28 26 24 22
2
4
6
8
x
22
R
24
J
26
Q
28
4. Determine whether nQRS is congruent to nXYZ by SAS.
y
8
Q
5
R
6
4
S
2
0
28 26 24 22
2
4
6
8
x
22
24
Z
26
Y
28
X
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Lesson 5.4 вЂѓ Skills Practice
page 4
5. Determine whether nJKL is congruent to nMNP by SAS.
y
K
8
J
6
4
L
2
0
28 26 24 22
2
4
6
8
x
22
P
24
M
26
28
N
5
542вЂѓ
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Lesson 5.4 вЂѓ Skills Practice
page 5
Name
Date
6. Determine whether nATV is congruent to nDNP by SAS.
y
T
8
A
6
4
2
V
0
28 26 24 22
2
4
6
8
22
24
x
N
D
26
28
P
5
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Lesson 5.4 вЂѓ Skills Practice
page 6
Perform the transformation described on each given triangle. Then, verify that the triangles are congruent
by SAS. Use the Distance Formula and a protractor when necessary.
7. Reflect nABC over the y-axis to form nXYZ. Verify that nABC > nXYZ by SAS.
AB 5 XY 5 5
y
A
B
Y
8
AC 5 XZ 5 5
m/A 5 m/X 5 90В°
The triangles are congruent by the SAS
CongruenceВ Theorem.
X
6
4
C
Z
2
0
28 26 24 22
2
4
6
x
8
22
24
26
28
8. Translate nDEF 11 units to the left and 10 units down to form nQRS. Verify that nDEF > nQRS by SAS.
y
8
D
6
5
4
F
E
2
0
28 26 24 22
2
4
6
8
x
22
26
28
544вЂѓ
24
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Lesson 5.4 вЂѓ Skills Practice
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Name
Date
9. Rotate nJKL 180В° counterclockwise about the origin to form nMNP. Verify that nJKL > nMNP by SAS.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
22
x
L
24
J
K
26
28
10. Reflect nAFP over the y-axis to form nDHW. Verify that nAFP > nDHW by SAS.
y
A
8
5
F
6
4
2
0
28 26 24 22
2
4
6
x
8
22
24
26
28
P
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Lesson 5.4 вЂѓ Skills Practice
page 8
11. Translate nACE 4 units to the right and 4 units down to form nJKQ. Verify that nACE > nJKQ by SAS.
y
A
8
E
C
6
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
5
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Lesson 5.4 вЂѓ Skills Practice
page 9
Name
Date
12. Rotate nBMZ 90В° counterclockwise about the origin to form nDRT. Verify that nBMZ > nDRT by SAS.
y
B
8
M
6
4
Z
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
5
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Lesson 5.4 вЂѓ Skills Practice
page 10
Determine the angle measure or side measure that is needed in order to prove that each set of triangles
are congruent by SAS.
13. In nART, AR 5 12, RT 5 8, and m/R 5 70В°. In nBSW, BS 5 12, and m/S 5 70В°.
SW 5 8
14. In nCDE, CD 5 7, and DE 5 11. In nFGH, FG 5 7, GH 5 11, and m/G 5 45В°.
15. In nJKL, JK 5 2, KL 5 3, and m/K 5 60В°. In nMNP, NP 5 3, and m/N 5 60В°.
16. In nQRS, QS 5 6, RS 5 4, and m/S 5 20В°. In nTUV, TV 5 6, and UV 5 4.
17.
T
Z
11 in.
15 in.
5
D
15 in.
65В°
18.
11 in.
W
R
K
L
8 ft
T
548вЂѓ
8 ft
M
X
20 ft
N
B
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Lesson 5.4 вЂѓ Skills Practice
page 11
Name
Date
19.
A
O
7m
C
50В°
7m
6m
G
6m
D
T
20.
V
E
14 ft
R
35В°
P
5
12 ft
12 ft
W
35В°
M
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Lesson 5.4 вЂѓ Skills Practice
page 12
Determine whether there is enough information to prove that each pair of triangles are congruent by SSS
or SAS. Write the congruence statements to justify your reasoning.
?
?
21. nMNP > вЂ‰nPQM
22. nWXY > вЂ‰nZYX
W
N
X
30В°
18 in.
10 in.
7 ft
M
7 ft
P
10 in.
30В°
Y
18 in.
Z
Q
The triangles are congruent by SSS.
____ ___
___ ____
NPвЂЇвЂ‹
вЂ‹ вЂЇ> QMвЂЇвЂ‹
вЂ‹ вЂЇ
____ ____
MPвЂЇвЂ‹
вЂ‹ вЂЇ> PMвЂЇвЂ‹
вЂ‹ вЂЇ
MNвЂЇвЂ‹
вЂ‹ вЂЇ> PQвЂЇвЂ‹
вЂ‹ вЂЇ
?
?
23. nBCE > вЂ‰nDAF
24. nHJM > вЂ‰nMKH
J
B
A
F
2 cm
2 cm
E
C
H
D
550вЂѓ
M
5
K
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Lesson 5.4 вЂѓ Skills Practice
page 13
Name
Date
?
?
25. nPQR > вЂ‰nSTW
26. nMAT > вЂ‰nMHT
S
Q
A
T
R
M
P
T
W
?
?
27. nBDW > вЂ‰nBRN
5m
H
28. nABC > вЂ‰nEDC
D
3m
N
A
B
B
C
5m
D
3m
W
E
R
5
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5
552вЂѓ
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Lesson 5.5 вЂѓ Skills Practice
Name
Date
Angle to the Left of Me, Angle to the Right of Me
Angle-Side-Angle Congruence Theorem
Vocabulary
Describe how to prove the given triangles are congruent. Use the Angle-Side-Angle Congruence Theorem
1.
y
8
P
N
6
4
2
M
0
28 26 24 22
A
2
4
6
8
x
22
24
26
C
28
B
5
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Lesson 5.5 вЂѓ Skills Practice
page 2
Problem Set
Determine whether each pair of given triangles are congruent by ASA. Use the Distance Formula and a
protractor when necessary.
1. Determine whether nABC is congruent to nDEF by ASA.
m/B 5 m/E 5 90В°
m/C 5 m/F 5 45В°
y
A
8
BC 5 EF 5 5
The triangles are congruent by the ASA
Congruence Theorem.
6
4
B
C
2
0
28 26 24 22
2
22
4
6
x
8
E
D
24
26
28
F
2. Determine whether nNPQ is congruent to nRST by ASA.
y
5
N
8
6
Q
P
2
0
28 26 24 22
S
2
22
24
26
4
6
8
x
4
28
R
554вЂѓ
T
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Lesson 5.5 вЂѓ Skills Practice
page 3
Name
Date
3. Determine whether nAGP is congruent to nBHQ by ASA.
y
P
8
6
4
A
G
2
0
28 26 24 22
2
4
6
8
x
22
Q
24
26
28
H
B
4. Determine whether nCKY is congruent to nDLZ by ASA.
y
8
5
C
K
6
Z
4
2
0
28 26 24 22
2
4
6
8
x
22
24
Y
26
D
L
28
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Lesson 5.5 вЂѓ Skills Practice
page 4
5. Determine whether nFMR is congruent to nJQW by ASA.
y
M
8
6
R
4
2
F
28 26 24 22
0
J
22
2
24
4
6
x
8
W
26
28
Q
6. Determine whether nGHJ is congruent to nKLM by ASA.
y
G
8
5
H
6
4
L
2
0
28 26 24 22
4
6
x
8
22
24
26
M 28
K
556вЂѓ
J
2
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Lesson 5.5 вЂѓ Skills Practice
page 5
Name
Date
Perform the transformation described on each given triangle. Then, verify that the triangles are congruent
by ASA. Use the Distance Formula and a protractor when necessary.
7. Reflect nABC over the y-axis to form nXYZ. Verify that nABC > nXYZ by SAS.вЂѓ
m/C 5 m/Z 5 90В°
m/A 5 m/X 5 63В°
y
8
AC 5 XZ 5 3
6
The triangles are congruent by the ASA
Congruence Theorem.
4
2
0
28 26 24 22
2
22
X
4
6
x
8
A
24
Y
26
Z
C
B
28
8. Rotate nDEF 90В° clockwise about the origin to form nQRS. Verify that nDEF > nQRS by SAS.вЂѓ
y
5
D
8
6
4
E
F
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
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Lesson 5.5 вЂѓ Skills Practice
page 6
9. Translate nHMZ 6 units to the right and 10 units up to form nBNY. Verify that nHMZ > nBNY
by ASA.вЂ‚
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
H
24
26
M
Z
28
10. Reflect nAFP over the y-axis to form nDHW. Verify that nAFP > nDHW by ASA.
y
5
A
F
8
6
4
0
28 26 24 22
2
22
P
24
26
28
558вЂѓ
4
6
8
x
2
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Lesson 5.5 вЂѓ Skills Practice
page 7
Name
Date
11. Rotate nACE 180В° counterclockwise about the origin to form nJKQ. Verify that nACE > nJKQ by SAS.
y
C
8
6
4
A
2
E
0
28 26 24 22
2
4
6
8
x
22
24
26
28
12. Reflect nJKL over the x-axis to form nMNP. Verify that nJKL > nMNP by ASA.
y
J
5
8
K
6
L
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
28
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Lesson 5.5 вЂѓ Skills Practice
page 8
Determine the angle measure or side measure that is needed in order to prove that each set of triangles
are congruent by ASA.
13. In nADZ, m/A 5 20В°, AD 5 9, and m/D 5 70В°. In nBEN, BE 5 9, and m/E 5 70В°.
m/B 5 20В°
14. In nCUP, m/U 5 45В°, and m/P 5 55В°. In nHAT, AT 5 14, m/A 5 45В°, and m/T 5 55В°.
15. In nHOW, m/H 5 10В°, HW 5 3, and m/W 5 60В°. In nFAR, FR 5 3, and m/F 5 10В°.
16. In nDRY, m/D 5 100В°, DR 5 25, and m/R 5 30В°. In nWET, m/W 5 100В°, and m/E 5 30В°.
17. B
D
W
T
8 ft
40В°
R
Z
8 ft
18. K
M
30В°
7 in.
60В°
X
30В°
60В°
T
560вЂѓ
L
N
5
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Lesson 5.5 вЂѓ Skills Practice
page 9
Name
Date
19.
G
R
F
18 m
60В°
18 m
W
70В°
70В°
Z
S
20. A
T
P
40В°
5 in.
85В°
5
85В°
40В°
M
X
D
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5
562вЂѓ
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Lesson 5.6 вЂѓ Skills Practice
Name
Date
Sides Not Included
Angle-Angle-Side Congruence Theorem
Vocabulary
Describe how to prove the given triangles are congruent. Use the Angle-Angle-Side Congruence Theorem
y
1.
B
C
8
6
4
A
2
0
28 26 24 22
22
2
4
6
8
x
X
24
26
28
Z
Y
5
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Lesson 5.6 вЂѓ Skills Practice
page 2
Problem Set
Determine whether each set of given triangles are congruent by AAS. Use the Distance Formula and a
protractor when necessary.
1. Determine whether nABC is congruent to nDEF by AAS.
m/A 5 m/D 5 45В°
y
A
m/B 5 m/E 5 45В°
8
BC 5 EF 5 7
6
The triangles are congruent by the AAS
Congruence Theorem.
4
C
B
2
0
28 26 24 22
22
2
D
4
6
8
x
F
24
26
28
E
2. Determine whether nGHJ is congruent to nKLM by AAS.
5
y
G
8
6
2
J
0
28 26 24 22
L
H
2
22
4
M
24
6
8
x
4
26
28
K
564вЂѓ
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Lesson 5.6 вЂѓ Skills Practice
page 3
Name
Date
3. Determine whether nAGP is congruent to nBHQ by AAS.
y
8
G
Q
6
B
4
2
0
28 26 24 22
2
4
6
8
x
22
24
A
P
26
H
28
4. Determine whether nCKY is congruent to nDLZ by AAS.
y
C
8
5
6
4
Y
0
28 26 24 22
L
K
2
22
2
4
6
8
x
Z
24
26
28
D
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Lesson 5.6 вЂѓ Skills Practice
page 4
5. Determine whether nFMR is congruent to nJQW by AAS.
y
F
M
8
6
4
R
2
0
28 26 24 22
2
4
6
8
x
22
W
24
26
J
28
Q
6. Determine whether nNPQ is congruent to nRST by AAS.
y
P
T
8
5
6
N
4
2
0
28 26 24 22
2
4
6
8
x
24
R
26
Q
566вЂѓ
28
S
22
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Lesson 5.6 вЂѓ Skills Practice
page 5
Name
Date
Perform the transformation described on each given triangle. Then, verify that the triangles are congruent
by AAS. Use the Distance Formula and a protractor when necessary.
7. Reflect nABC over the y-axis to form nXYZ. Verify that nABC > nXYZ by AAS.
m/B 5 m/Y 5 76В°
y
m/C 5 m/Z 5 90В°
8
X
AC 5 XZ 5 12
6
A
The triangles are congruent by the AAS
Congruence Theorem.
4
2
0
28 26 24 22
2
4
6
8
x
22
24
26
Y
Z
C
28
B
8. Translate nDEF 11 units to the left and 11 units down to form nQRS. Verify that nDEF > nQRS by AAS.
y
5
D
8
6
4
2
F
0
28 26 24 22
2
E
4
6
8
x
22
24
26
28
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Lesson 5.6 вЂѓ Skills Practice
page 6
9. Rotate nJKL 180В° counterclockwise about the origin to form nMNP. Verify that nJKL > nMNP by AAS.
y
8
6
4
2
0
28 26 24 22
K
2
4
22
6
8
x
L
24
26
J
28
10. Translate nCUP 9 units to the left and 4 units up to form nJAR. Verify that nCUP > nJAR by AAS.
y
8
6
5
4
U
2
0
28 26 24 22
2
4
6
8
x
24
26
28
568вЂѓ
C
P
22
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Name
Date
11. Reflect nAFP over the x-axis to form nDHW. Verify that nAFP > nDHW by AAS.
y
8
6
4
2
0
28 26 24 22
2
4
6
8
x
22
F
24
26
A
28
P
5
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12. Rotate nACE 270В° counterclockwise about the origin to form nJKQ. Verify that nACE > nJKQ
by AAS.
y
8
C
6
A
4
2
0
28 26 24 22
2
4
6
8
x
22
24
E
26
28
Determine the angle measure or side measure that is needed in order to prove that each set of triangles
are congruent by AAS.
5
13. In nANT, m/A 5 30В°, m/N 5 60В°, and NT 5 5. In nBUG, m/U 5 60В°, and UG 5 5.
m/B 5 30В°
15. In nEMZ, m/E 5 40В°, EZ 5 7, and m/M 5 70В°. In nDGP, DP 5 7, and m/D 5 40В°.
14. In nBCD, m/B 5 25В°, and m/D 5 105В°. In nRST, RS 5 12, m/R 5 25В°, and m/T 5 105В°.
16. In nBMX, m/M 5 90В°, BM 5 16, and m/X 5 15В°. In nCNY, m/N 5 90В°, and m/Y 5 15В°.
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Name
Date
17.
B
D
18 in.
18 in.
T
40В°
R
40В°
70В°
W
Z
18.
K
X
60В°
30В°
T
3 ft
N
30В°
60В°
M
L
5
19.
F
S
50В°
60В°
W
25 m
Z
60В°
50В°
R
G
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20. A
D
20 in.
30В°
110В°
P
20 in.
30В°
M
X
T
Determine whether there is enough information to prove that each pair of triangles are congruent by ASA
or AAS. Write the congruence statements to justify your reasoning.
?
?
22. nEFG > nHJK
21. nABD > nCBD
F
B
A
J
C
D
The triangles are congruent by AAS.
E
K
H
G
___ ___
BDвЂЇвЂ‹
вЂ‹ вЂЇ> BDвЂЇвЂ‹
вЂ‹ вЂЇ
?
?
24. nRST > nWZT
23. nMNQ > nPQN
N
W
P
S
M
Q
R
572вЂѓ
T
Z
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Name
Date
?
?
25. nBDM > nMDH
26. nFGH > nJHG
D
F
J
G
H
55В° 55В°
B
H
60В°
60В°
M
?
?
28. nRST > nWXY
27. nDFG > nJMT
D
M
65В°
W
S
T
50В°
R
4 ft
4 ft
3 cm
70В°
70В°
50В°
65В°
F
G
T
J
5
3 cm
X
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Lesson 5.7 вЂѓ Skills Practice
Name
Date
Any Other Theorems You Forgot to Mention?
Using Congruent Triangles
Problem Set
Construct a perpendicular bisector to each line segment. Connect points on the bisector on either side of
the line segment to form the new line segment indicated.
____
___
1. MNвЂ‹
вЂ‹ вЂЇbisected by PRвЂ‹
вЂ‹ вЂЇat point Q
P
Q
M
N
R
___
5
____
2. HJвЂ‹
вЂ‹ вЂЇbisected by KMвЂ‹
вЂ‹ вЂЇat point L
H
J
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___
___
___
___
4.вЂ‹PQвЂ‹вЂЇbisected by RTвЂ‹
вЂ‹ вЂЇat point S
вЂ‹ вЂЇat point D
3. ABвЂ‹
вЂ‹ вЂЇbisected by CEвЂ‹
page 2
A
P
B
___
Q
___
___
____
6.вЂ‹STвЂЇвЂ‹вЂЇbisected by UWвЂ‹
вЂ‹ вЂЇat point V
5. FGвЂ‹
вЂ‹ вЂЇbisected by HKвЂ‹
вЂ‹ вЂЇat point J
F
T
G
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S
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Lesson 5.7 вЂѓ Skills Practice
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Name
Date
Use a triangle congruence theorem to complete each proof. Some of the statements and reasons are
provided for you.
___
___
7. Given: HKвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of FJвЂ‹
вЂ‹ вЂЇat point J
Prove: Point H is equidistant to points F and G
H
J
F
G
K
___ ___ ___
___
1.вЂ‚ FGвЂЇвЂ‹
вЂ‹ вЂЇ' HKвЂЇвЂ‹
вЂ‹ вЂЇ
, HKвЂЇвЂ‹
вЂ‹ вЂЇbisects FGвЂЇ
вЂ‹ вЂЇ
вЂ‹
1.вЂ‚Definition of perpendicular bisector
2.вЂ‚ /FJH and /GJH are right angles.
2.вЂ‚ Definition of perpendicular lines
3.вЂ‚ /FJH оЂѕ /GJH
3.вЂ‚ All right angles are congruent.
___
___
4.вЂ‚ FJвЂЇвЂ‹
вЂ‹ вЂЇоЂѕ GJвЂЇвЂ‹
вЂ‹ вЂЇ
4.вЂ‚ Definition of bisect
5.вЂ‚ HJвЂЇ
вЂ‹ вЂЇ
вЂ‹оЂѕ HJвЂЇ
вЂ‹ вЂЇ
вЂ‹
5.вЂ‚ Reflexive Property
6.вЂ‚ nFJH оЂѕ nGJH
6.вЂ‚ SAS Congruence Theorem
___ ___
___ ____
7.вЂ‚вЂ‹FHвЂЇвЂЇ
вЂ‹оЂѕ GHвЂЇвЂ‹
вЂ‹ вЂЇ
8.вЂ‚Point H is equidistant to points
F and G
7.вЂ‚Corresponding sides of congruent
triangles are congruent
8.вЂ‚ Definition of equidistant
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___
____
вЂ‹ вЂЇat point N
8. Given: PMвЂЇвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of STвЂЇвЂ‹
Prove: Point M is equidistant to points S and T
P
S
N
T
M
1.вЂ‚Definition of perpendicular bisector
2.вЂ‚
2.вЂ‚ Definition of perpendicular lines
3.вЂ‚
3.вЂ‚ All right angles are congruent.
4.
4.вЂ‚
5.
5.вЂ‚
6.вЂ‚
6.вЂ‚
7.
7.вЂ‚
8.вЂ‚Point M is equidistant to points
S and T
8.вЂ‚ Definition of equidistant
5
1.вЂ‚
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Name
Date
___
____
9. Given: CAвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of UWвЂ‹
вЂ‹ вЂЇat point B
Prove: Point C is equidistant to points U and W
U
C
B
A
W
____
___ ___
____
1.вЂ‚Definition of perpendicular bisector
2.вЂ‚
2.вЂ‚
3.вЂ‚
3.вЂ‚ All right angles are congruent.
4.
4.вЂ‚ Definition of bisect
5.
5.вЂ‚
6.вЂ‚
6.вЂ‚
7.
7.вЂ‚ Corresponding sides of congruent
triangles are congruent
8.вЂ‚
8.вЂ‚
5
1.вЂ‚ UWвЂЇвЂ‹
вЂ‹ вЂЇ' CAвЂЇвЂ‹
вЂ‹ вЂЇ
, CAвЂЇвЂ‹
вЂ‹ вЂЇbisects UWвЂЇвЂ‹
вЂ‹ вЂЇ
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___
page 6
___
вЂ‹ вЂЇat point R
10. Given: TKвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of LMвЂ‹
Prove: Point T is equidistant to points L and M
L
T
R
K
M
1.
1.вЂ‚
2.вЂ‚
2.вЂ‚ Definition of perpendicular lines
3.вЂ‚
3.вЂ‚ All right angles are congruent.
4.
4.вЂ‚
___
5.вЂ‚ Reflexive Property
6.вЂ‚
6.вЂ‚
7.
7.вЂ‚ 8.вЂ‚
8.вЂ‚ Definition of equidistant
5
___
5.вЂ‚вЂ‹TRвЂЇвЂ‹вЂЇоЂѕ TRвЂЇвЂ‹
вЂ‹ вЂЇ
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Name
Date
___
___
11. Given: HTвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of UVвЂ‹
вЂ‹ вЂЇat point P
Prove: Point H is equidistant to points U and V
V
H
P
T
U
1.
1.вЂ‚
2.вЂ‚ /UPH and /VPH are right angles.
2.вЂ‚ Definition of perpendicular lines
3.вЂ‚
3.вЂ‚
4.
4.вЂ‚ Definition of bisect
5.
5.вЂ‚
6.вЂ‚
6.вЂ‚
7.
7.вЂ‚ 8.вЂ‚
8.вЂ‚
5
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___
____
вЂ‹ вЂЇat point V
12. Given: UWвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of CDвЂ‹
Prove: Point U is equidistant to points C and D
C
U
V
W
D
1.вЂ‚Definition of perpendicular bisector
2.вЂ‚
2.вЂ‚
3.вЂ‚ /CVU оЂѕ /DVU
3.вЂ‚ All right angles are congruent.
4.
4.вЂ‚
5.
5.вЂ‚
6.вЂ‚
6.вЂ‚
7.
7.вЂ‚ Corresponding sides of congruent
triangles are congruent
8.вЂ‚
8.вЂ‚
5
1.
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Name
Date
Complete each diagram to provide a counterexample that proves the indicated theorem does not work for
congruent triangles. Explain your reasoning. A hint is provided in each case.
13. Angle-Angle-Angle (Hint: Use vertical angles.)
D
A
C
B
___
___
xtend ACвЂЇвЂ‹
E
вЂ‹ вЂЇand
вЂ‹ вЂЇ
, and connect
___BCвЂЇвЂ‹
___points D
and E so that ABвЂЇвЂ‹
вЂ‹ вЂЇis parallel to DEвЂЇвЂ‹
вЂ‹ вЂЇ
. Since
vertical angles are congruent, all three
corresponding angles of the two triangles
are congruent. The side lengths, however,
are different, so nABC is not congruent
to nDEC.
E
14. Side-Side-Angle (Hint: Draw a triangle that shares /P with the given triangle.)
Q
5
P
R
15. Angle-Angle-Angle (Hint: Draw a triangle that shares /T with the given triangle.)
T
S
U
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16. Side-Side-Angle (Hint: Draw a triangle that shares /L with the given triangle.)
L
K
M
17. Angle-Angle-Angle (Hint: Draw a triangle that has an angle with the same measure as /E.)
E
D
18. Side-Side-Angle (Hint: Draw a triangle that shares /U with the given triangle.)
T
U
V
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Name
Date
State the congruence theorem that proves the triangles in each diagram are congruent. If not enough
information is given, name an example of information that could be given that you could use to prove
____
____
W
19. Given: VвЂ‰WвЂЇвЂ‹
вЂ‹ вЂЇоЂѕ XWвЂЇвЂ‹
вЂ‹ вЂЇ
Prove: nVYW оЂѕ nXYW
Not enough information is given.
If /VWY оЂѕ /XWY is given, then nVYW оЂѕ nXYW
by the SAS Triangle Congruence Theorem.
V
___
___
X
Y
C
20. Given: CEвЂ‹
вЂ‹ вЂЇis a perpendicular bisector of FDвЂ‹
вЂ‹ вЂЇ
D
Prove: nFEC оЂѕ nDEC
E
5
F
___
___
21. Given: /WST оЂѕ /VUT, STвЂЇвЂ‹
вЂ‹ вЂЇоЂѕ UTвЂЇвЂ‹
вЂ‹ вЂЇ
S
U
Prove: nWST оЂѕ nVUT
T
W
V
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___
page 12
___
вЂ‹ вЂЇ
22. Given: nABD is isosceles with ABвЂЇвЂ‹
B
C
A
____
___ ___
___
D
H
23. Given: GHвЂЇвЂ‹
вЂ‹ вЂЇоЂѕ JKвЂЇвЂ‹
вЂ‹ вЂЇ, HJвЂЇвЂ‹
вЂ‹ вЂЇоЂѕ KGвЂЇвЂ‹
вЂ‹ вЂЇ
Prove: nGHK оЂѕ nJKH
G
J
K
5
___
___
24. Given: PTвЂЇвЂ‹
вЂ‹ вЂЇоЂѕ SRвЂЇвЂ‹
вЂ‹ вЂЇ
, /PQT оЂѕ /RQS P
R
T
586вЂѓ
Q
S
Prove: nTPQ оЂѕ nSRQ
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