Podcast
Questions and Answers
If the smallest angle of rotation for a regular polygon is 18°, how many sides does the polygon have?
If the smallest angle of rotation for a regular polygon is 18°, how many sides does the polygon have?
20
Which set of side lengths represents a triangle with 3 lines of reflectional symmetry?
Which set of side lengths represents a triangle with 3 lines of reflectional symmetry?
5, 5, 5
Which figure shows a line of reflectional symmetry for the letter T?
Which figure shows a line of reflectional symmetry for the letter T?
Figure C
What is the order of rotational symmetry for a rhombus?
What is the order of rotational symmetry for a rhombus?
A regular polygon has 15 sides. What is a possible angle of rotational symmetry for the figure?
A regular polygon has 15 sides. What is a possible angle of rotational symmetry for the figure?
How many lines of reflectional symmetry does an equilateral triangle have?
How many lines of reflectional symmetry does an equilateral triangle have?
Which triangle has 0 reflectional symmetries?
Which triangle has 0 reflectional symmetries?
Which letter in the word HAPPY has an order 2 rotational symmetry?
Which letter in the word HAPPY has an order 2 rotational symmetry?
Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.
Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.
Which figure has an order 3 rotational symmetry?
Which figure has an order 3 rotational symmetry?
What is the smallest angle of rotational symmetry for a square?
What is the smallest angle of rotational symmetry for a square?
How can a regular hexagon be folded to show that it has reflectional symmetry?
How can a regular hexagon be folded to show that it has reflectional symmetry?
If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, which statement would be true?
If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, which statement would be true?
Which figure has the same order of rotational symmetry as a rectangle?
Which figure has the same order of rotational symmetry as a rectangle?
Which type of triangle will always have exactly 1-fold reflectional symmetry?
Which type of triangle will always have exactly 1-fold reflectional symmetry?
Which angle of rotation is an angle of rotational symmetry for all figures?
Which angle of rotation is an angle of rotational symmetry for all figures?
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Study Notes
Regular Polygon Symmetry
- A regular polygon with a smallest angle of rotation of 18° has 20 sides.
- A regular polygon with 15 sides has a rotational symmetry angle of 72°.
- The smallest angle of rotational symmetry for a square is 90°.
Reflectional Symmetry in Triangles
- An equilateral triangle has 3 lines of reflectional symmetry.
- A triangle with side lengths of 5, 5, and 5 shows 3 lines of reflectional symmetry, making it an equilateral triangle.
- An isosceles triangle has exactly 1 line of reflectional symmetry.
Rotational Symmetry
- A rhombus has an order of rotational symmetry of 2.
- An equilateral triangle possesses order 3 rotational symmetry.
- The letter H in "HAPPY" features order 2 rotational symmetry.
- A rhombus shares the same order of rotational symmetry as a rectangle.
Lines of Symmetry
- A regular pentagon has multiple lines of symmetry: each bisects a vertex angle and a side, and is perpendicular to a side.
- A quadrilateral with exactly 2 lines of symmetry, both being angle bisectors, is a rhombus due to its congruent angles.
Reflectional Symmetry in Letters
- The letter T has a line of reflectional symmetry indicated in Figure C.
General Symmetry Facts
- An angle of rotational symmetry applicable to all figures is 360°.
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