Student Name
Class / Section
Grade / Year
Teacher
School
Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
A scalene triangle has no line of symmetry.
(1 pt)
2.
A rectangle has exactly one line of symmetry.
(1 pt)
3.
A regular hexagon has rotational symmetry of order 6.
(1 pt)
4.
A kite always has two lines of symmetry.
(1 pt)
5.
A circle has rotational symmetry for every angle of rotation.
(1 pt)
6.
A generic parallelogram (that is not a rectangle or rhombus) has no line of symmetry.
(1 pt)
7.
Folding a figure along one of its lines of symmetry will make the two halves coincide.
(1 pt)
8.
The smallest angle of rotation for a regular pentagon is 60°.
(1 pt)
9.
An equilateral triangle has exactly two lines of symmetry.
(1 pt)
10.
The uppercase letters M and W (in standard block style) have the same number of lines of symmetry.
(1 pt)
11.
Which shape has no line of symmetry but has rotational symmetry of order 2?
(2 pts)
C. Parallelogram (not a rectangle)
12.
What is the smallest angle that maps a regular octagon to itself?
(2 pts)
13.
How many lines of symmetry does a regular five-pointed star (pentagram) have?
(2 pts)
14.
An isosceles triangle with a horizontal base has which line of symmetry?
(2 pts)
A. A vertical line through the apex and midpoint of the base
B. A horizontal line along the base
C. A diagonal line through one side
15.
What is the order of rotational symmetry of a square?
(2 pts)
16.
How many lines of symmetry does a regular dodecagon have?
(2 pts)
17.
If the smallest angle of rotation for a figure is 120°, what is the order of its rotational symmetry?
(2 pts)
18.
Which statement is true for a rhombus that is not a square?
(2 pts)
A. It has exactly two lines of symmetry (its diagonals) and rotational order 2.
B. It has no line of symmetry and rotational order 1.
C. It has four lines of symmetry and rotational order 4.
D. It has one line of symmetry and rotational order 3.
19.
Which transformation makes a figure coincide with itself across a symmetry line?
(2 pts)
B. Reflection over that line
C. Rotation about a corner
20.
Which shape has exactly one line of symmetry and no rotational symmetry (other than a full turn)?
(2 pts)
21.
The smallest angle that maps a square onto itself is
degrees.
(2 pts)
22.
A figure that looks unchanged after a half-turn has rotational symmetry of order
.
(2 pts)
23.
An equilateral triangle has
lines of symmetry.
(2 pts)
24.
A regular n-gon has
lines of symmetry.
(2 pts)
25.
Reflecting a shape across its line of symmetry produces two
halves.
(2 pts)
26.
A circle has an
number of lines of symmetry.
(2 pts)
27.
The angle between adjacent spokes in a 12-spoke wheel is
degrees.
(2 pts)
28.
A generic parallelogram (not a rectangle or rhombus) has
line(s) of symmetry.
(2 pts)
29.
The smallest angle of rotation for a regular pentagon is
.
(2 pts)
30.
Folding along a line of symmetry makes the two sides
.
(2 pts)
31.
A festival logo shows 8 identical petals equally spaced around a center. (a) What is the order of rotational symmetry? (b) What is the smallest angle that maps the logo onto itself? Show your working.
(5 pts)
32.
A regular polygon has each interior angle measuring 140°. Find (a) the number of sides, (b) the number of lines of symmetry, and (c) the smallest angle of rotation. Show your working.
(5 pts)
33.
A pattern looks the same after a rotation of 24°. How many distinct orientations will it have in one full turn, and what is its order of rotational symmetry? Show your working.
(5 pts)
34.
A wheel has 18 evenly spaced spokes. (a) What is the smallest non-zero angle that maps it onto itself? (b) How many rotational symmetries does it have (including the full turn)? Show your working.
(5 pts)
35.
A badge shows 10 identical points arranged evenly around a center (like a starburst). Determine (a) the order of rotational symmetry, (b) the smallest angle of rotation, and (c) the number of lines of symmetry if the points are placed at equal angles. Show your working.
(5 pts)
36.
A designer wants a logo that repeats perfectly after every 30° turn. (a) How many identical sectors will the logo have? (b) What is its rotational symmetry order? Show your working.
(5 pts)
37.
A square sheet is folded along its vertical line of symmetry. A single hole is punched 3 cm to the right of the fold. After unfolding, how many holes appear, and where are they relative to the fold? Show your working.
(5 pts)
38.
A regular polygon has rotational symmetry of order 9. Find (a) the angle of each step of rotation, and (b) the number of lines of symmetry. Show your working.
(5 pts)
39.
A clock face is redesigned with 12 identical marks (no numbers). Determine (a) the order of rotational symmetry, and (b) the smallest rotation that maps it onto itself. Show your working.
(5 pts)
40.
Each interior angle of a regular polygon is 165°. Find (a) the number of sides, (b) the number of lines of symmetry, and (c) the smallest angle of rotation. Show your working.
(5 pts)