Download Answers for the lesson “Perform Congruence Transformations”

LESSON
4.9
Answers for the lesson “Perform Congruence
Transformations”
Skill Practice
11.
y
1. Subtract 1 from each
x-coordinate and add 4 to
each y-coordinate.
1
2. The image is congruent to
21
the original figure.
3. translation
4. rotation
5. reflection
6. yes
7. no
8. yes
9.
x
12.
y
y
1
1
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21
x
21
x
13. (x, y) l (x 2 4, y 2 2)
14. (x, y) l (x 1 6, y 1 3)
y
10.
15. (x, y) l (x 1 2, y 2 1)
1
21
x
16. (x, y) l (x 2 7, y 1 9)
17.
y
1
21
x
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129
18.
y
21.
y
C
1
1
21
D
21
x
x
B
A
19.
y
not a rotation
22.
1
21
y
D
x
C
1
A
21
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20.
y
1
21
x
B
B
A
not a rotation
x
C
y
23.
A
D
rotation; 908 clockwise
1
21
C
B
x
D
not a rotation
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130
24. The red triangle rotation segment
40. a. Sample answer: MOM, TOT
should connect corresponding
angles of the triangle; the red
triangle is rotated 908 clockwise.
25. Yes; take any point or any line
segment and rotate 3608.
MOM
b. Sample answer: HI, OH
HI
y
P
3
360
3
TOT
OH
41. a. (x, y) l (x 2 1, y 1 2)
x
360
b. (x, y) l (x 1 2, y 2 1)
c. No; the translation needed does
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not match a knight’s move.
26. (2, 2)
27. (3, 4)
28. (21, 0)
29. (2, 3)
30. (3, 5)
31. (13, 25)
32. The corresponding sides of each
triangle are congruent therefore
the triangles are congruent.
33. }
UV
34. }
AV
35. nDST
36. n XYC
37. m 5 3, n 5 11, a 5 2,
1
g 5 2, h 5 }4
Problem Solving
38. a. The designer can reflect the
layout over the horizontal line.
b. 4 ft
} and EF
} are
42. The slopes of BC
both 21 and the slopes of
} and DE
} are both 1. Therefore,
AB
}> }
AB
BC since the product of
their slopes is 21. Similarly,
} > EF
}. Thus n ABC and
DE
n DEF are right triangles.
Using the distance
formula,
}
BC 5 EF 5 Ï2}and
AC 5 DF 5 Ï10 . So,
} > EF
} > DF
}, AC
}. By the HL
BC
Congruence Theorem,
n ABC > n DEF. Therefore,
n DEF is a congruence
transformation of n ABC,
described by the notation
(x, y) l (x 2 5, y 1 1).
43. B
39. 908 clockwise,
908 counterclockwise
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131
44. (1, 4), (1, 1), (3, 1); no; the final
5. a. In n ABC, it is given that
}
AB > }
CB, therefore
image would have a different
rotation segment.
Mixed Review of
Problem Solving
Ž BCE > Ž BAE by the
Base Angles Theorem.
b. Sample answer:
n ABE > nCBE by AAS.
}
CE > }
AE by corr. parts of
s are > . n FAE > n DCE
>n
by ASA and therefore
}
AF > }
CD by corr. parts of >
s are >.
n
1. a. reflection in the y-axis
b. rotation of 908
counterclockwise
c. reflection in the x-axis
d. Rotate figure A 908 clockwise
and 1808.
6. 7;
7
2. No; the given angle is not the
included angle.
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3. The length of the side forming the
348 angle with side measuring
8 centimeters, the angle the
third side makes with the side
measuring 8 centimeters, or
the angle the third side makes
with the side forming the 348
angle with the side measuring
8 centimeters
4. Yes; yes; Ž ACD and Ž BCE
are vertical angles so they are
congruent which makes
n ACD > n BCE by SAS. Since
} > BE
} by
n ACD > n BCE, AD
s are > .
corr. parts of > n
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