Chapter Review
(pp. 373–377)
9. Answers vary. Sample:
1. This figure has 9-fold rotation symmetry.
2. This figure has 9-fold rotation and reflection
symmetry.
10. Answers vary. Sample:
3. This figure has 12-fold rotation symmetry.
4.
11. Answers vary. Sample:
5.
12. Answers vary. Sample:
6.
13. 133, 23.5, and 23.5.
14. 5.5"
15. 20
16. m∠B = m∠C = 62
A
7. Answers vary. Sample:
B
C
m∠B = 68, m∠C = 56
A
8. Answers vary. Sample:
B
C
17. 36
A109
Geometry
18. 46
38. none
19. 134
39. a. By the Center of a Regular Polygon Theorem,
there is a unique point that is equidistant from
the vertices of an equilateral triangle. This
point is the center of the equilateral triangle
and of the circle in which it is inscribed. The
three angle bisectors of an equilateral triangle
are radii of this circle, so the three vertices
of the triangle are equidistant from their
intersection point, which must be the center of
the circle.
20. 69.5
21. 108
22. 54
1980 ≈
23. ____
152.308
13
24. m∠FEO = m∠DEO = m∠DGO = 64,
m∠GFO = m∠EFO = m∠GDO = m∠EDO = 26,
m∠FOG = m∠FOE = m∠EOD = m∠DOG = 90,
m∠GFE = m∠GDE = 52,
m∠FGD = m∠FED = 128
25. OE = 3 cm, OD = 6 cm, GE = 6 cm, FD = 12 cm
26. 116.7
27. a.
B
A
C
D
b. true
40. the base
41. The hypotenuse is always opposite the angle
with measure 90 in a right triangle. Because the
measures of the interior angles of a triangle add
to 180, the other two angles must have measures
less than 90. Thus, the hypotenuse must be the
longest side of a right triangle.
42.
b. m∠B = m∠D = 135, m∠C = 45
56.5°
6 cm
3 cm
28. ∠G, ∠A, ∠K
93.5°
29. Answers vary. Sample: EFLABCD and GFLKJIH
30°
5 cm
30. squares and rectangles
43. false
31. squares, rhombuses, and kites
44. false; Answers vary. Sample:
32. sometimes but not always
33. true
34. By the definition of midpoint, PM = PL and
is a symmetry line for the
QN = QO, so PQ
___
isosceles trapezoid and for LM. Therefore, by
is the
the Segment Symmetry Theorem,
PQ
___
___
___
perpendicular bisector of LM, so PQ ⊥ LM.
45. true
46. false; Answers vary. Sample:
35. true
36. false
47. parallelogram, rectangle, rhombus, square, kite
37. Regular Polygon Rotation Symmetry Theorem: A
regular n-gon has n-fold rotation symmetry.
Regular Polygon Reflection Symmetry Theorem:
A regular polygon has reflection symmetry about
every line containing its center and a vertex and
about every perpendicular bisector of its sides.
48. rhombus, square, kite
A110
Geometry
49. isosceles trapezoid, rectangle, square
50. Conclusions
1. TRAP is an isosceles
trapezoid
___ with___
bases TR and PA
and m∠R = m∠A
2. m∠R + m∠A = 180
3. m∠R = m∠A = 90
4. m∠T = m∠R and
m∠A = m∠P
5. m∠T = m∠P = 90
6. TRAP is a rectangle
____
Justifications
Given
Trapezoid Angle
Theorem
Substitution
Def. of isosceles
trapezoid
Substitution
Def. of rectangle
54. Answers vary. Sample:
55. The figure has 3-fold rotation symmetry.
___
51. Since MN and ⊥ OP, by the
Perpendicular
to Parallels Theorem,
___
____
MN ⊥ OP. Since m∠1 = m∠2, and m∠NOM =
bisects ∠NOM. By the Angle
m∠1 + m∠2, OP
is a symmetry line
Symmetry Theorem, OP
of ∠NOM. Since the only symmetry lines of a
segment are the line containing the segment and
the perpendicular bisector of the segment,
____ OP
must be the perpendicular bisector of MN.
By the definition of bisector, MP = NP.
52. It is given that
___ RSUT
___is an isosceles trapezoid
with bases RS and TU___
. By the
___ Isosceles
Trapezoid Theorem, TR US, and by the
definition of isosceles trapezoid, ∠S ∠R and
∠U___
∠T. Let m be the perpendicular bisector
of TU. m is the symmetry line of RSUT by the
Isosceles Trapezoid Symmetry Theorem. By the
definition of reflection, rm(S) = R and rm(U) = T.
Thus RU = ST by the Reflection Postulate.
53. Conclusions
1. O and P intersect
at A and B
2. OA = OB and
AP = BP
3. OAPB is a kite
56. The spider’s web has 20-fold rotation symmetry.
It also has 20 lines of reflection symmetry.
57. type 3
58. type 2
59. type 2
60. type 4
61.
polygon
quadrilateral
triangle
kite
isosceles
triangle
parallelogram
rhombus
equilateral
triangle
62.
polygon
quadrilateral
regular
polygon
Justifications
Given
All radii of the same
circle congruent.
Def. of kite
trapezoid
square
quadrilaterals
63.
quadrilaterals
with rotation
symmetry
rectangle
quadrilaterals
with at least one
symmetry line
kite
rhombus
square
A111
Geometry
quadrilaterals
with at least two
symmetry lines