Name ________________________________________ Date __________________ Class __________________
LESSON
17-4
Investigating Symmetry
Practice and Problem Solving: A/B
Use the figures on the grid to answer Problems 1−3.
1. What are the equations of the lines of
symmetry for figure A?
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2. Does figure B have line symmetry, rotational
symmetry, or both?
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3. If you rotate figure C all the way around point (7, 4), 50° at a time, will
you create a figure with rotational symmetry? Explain your answer.
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Tell whether each figure appears to have line symmetry, rotational
symmetry, both, or neither. If line symmetry, tell how many lines of
symmetry. If rotational symmetry, give the angle of rotational
symmetry.
4.
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5.
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6.
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7.
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Use principles of symmetry to answer Problems 8−9.
8. How many lines of symmetry does each quadrilateral have?
isosceles trapezoid ______ rectangle with sides 2-4-2-4 ______
square ______ rhombus ______
parallelogram with sides 2-4-2-4 and angles ≠ 90° ______
9. How many lines of symmetry does a regular pentagon have? ______
How many lines of symmetry does a regular hexagon have?______
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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LESSON 17-4
Practice and Problem Solving:
Modified
Practice and Problem Solving: A/B
1. yes
1. x = 4; y = 7
2. no
2. rotational symmetry.
3. yes
3. No. 360°÷ 50° is not a whole number, so
the points will not be evenly spaced all the
way around the center.
4. yes
5. B
4. both; 4 lines; 90°
6. A and B
5. line symmetry; 1 line
7. yes
6. rotational symmetry; 180°
7. both; 5 lines; 72°
8. isosceles trapezoid: 1; rectangle with
sides 2-4-2-4: 2; square: 4; rhombus: 2;
parallelogram with sides 2-4-2-4 and
angles ≠ 90°: 0
8. no
9. 5; 6
Practice and Problem Solving: C
1. Rotational. A rotation of 180° about the
center maps the figure to itself. However,
the side lengths are not the same (4 units
and 3 2 units), so there is no line that
divides the figure into two matching
halves.
2. y =
9. yes
1
x and y = −2x
2
3. The slopes are inverse reciprocals so the
lines are perpendicular. The figure is a
rhombus.
10. no
4. Rotational symmetry with angle of 180°;
no line symmetry
5. Possible answer: Reflect figure D over the
line x = 6. Then rotate the image 180°
about the point (6, −6).
6. Explanations will vary. Possible
explanation: Because all their sides are
congruent and all their angles are
congruent. A regular polygon can be
folded or rotated to match up congruent
sides and angles.
Reading Strategies
1. no
2. yes
7. 80°, 120°, 160°, 200°, 240°, 280°, 320°,
360°.
8. Possible answer: 7.2, 10, 12, 15, 18, 20,
22.5, 90. When they are divided into 360,
the quotient is a whole number.
3. yes; 120°
4. yes; 180°
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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