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Symmetry: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A figure has finite rotational order 14 about O, counting identity. Must it have point symmetry about O?

Answer choices for question 1 A No; only order 2 gives point symmetry B No; only circles have point symmetry C Yes; identity itself is a half-turn D Yes; seven least turns make a half-turn
2

A figure has finite rotational order 15 about O. Which candidate angle must match?

Answer choices for question 2 A $90^\circ$ B $72^\circ$ C $108^\circ$ D $180^\circ$
3

A report says a figure has finite rotational order and least positive matching angle $100^\circ$ . Which conclusion follows?

Answer choices for question 3 A The report is inconsistent with finite rotational order B The order is 100 C The order is 3, after rounding down D The order is 4, after rounding up
4

A circle has a single marked point on its boundary, and the mark is part of the figure. Which statement about rotations around the circle center is true?

Answer choices for question 4 A Every rotation still matches B A half-turn matches C Only identity matches the complete figure D A quarter-turn matches
5

The boundary of a square is symmetric under a half-turn. A short segment is then added from its center to the midpoint of its top side only. Does the new figure keep point symmetry about the center?

Answer choices for question 5 A No; the added segment turns to an absent bottom segment B Yes; the square boundary alone decides C Yes; the center is fixed D No; a half-turn changes segment length
6

For a finite-order figure, matching angles include $60^\circ$ and $180^\circ$ . No turn strictly between $0^\circ$ and $60^\circ$ matches. What is its order and point-symmetry status?

Answer choices for question 6 A Order 2, with point symmetry B Order 6, without point symmetry C Order 3, without point symmetry D Order 6, with point symmetry
7

A triangular outline joins $(0,0)$ , $(6,0)$ , and $(0,2)$ . A half-turn about $(3,0)$ swaps the first two vertices. Is that enough to establish point symmetry?

Answer choices for question 7 A Yes; two matching vertices decide every triangle B Yes; the turning center lies on a side C No; the third vertex maps to (6,-2), absent from the figure D No; both swapped vertices must be fixed
8

An exact figure has finite order 9 about O, including identity. Which statement explains why it has no point symmetry about O?

Answer choices for question 8 A Nine rotations include no identity B A half-turn would require 4.5 least turns, not an integer number C Its least angle is 9 degrees D No finite-order figure can have point symmetry
9

A candidate line divides a figure into equal areas. What extra fact would establish that it is a line of symmetry?

Answer choices for question 9 A It passes through any one boundary point B The two areas have the same numerical measure again C It is drawn vertically on the page D Reflection across it pairs every part of the entire figure
10

For a circle centered at O with positive radius, why does the finite-order least-angle formula fail?

Answer choices for question 10 A There is no finite count or least positive matching angle B A full turn is not 360 degrees for a circle C A circle cannot be rotated D Only its center belongs to the circle
11

A square boundary has letter labels at its corners used only as names. A quarter-turn moves each label name to a different named corner. Does that alone reject the square symmetry?

Answer choices for question 11 A Yes; every named point must be fixed B No; the names identify points and are not included decorations C Yes; names are always part of every figure D No; a quarter-turn fixes every point
12

A zero translation and a full-turn rotation are both recorded as symmetries of the same figure. How many distinct plane mappings do these two records describe?

Answer choices for question 12 A 0 B 2 C 1 D 360

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