Lines of Reflection and Angles of Rotation
In this activity, you will explore the angles of rotation of regular polygons and figures with rotational and reflectional symmetry. Work with your group to explore the rotations and reflections of your group's shape and answer the questions at the bottom of the page. [b]Learning Goal: [/b]Students will be able to describe rotations and reflections that carry a given rectangle, parallelogram, trapezoid, or regular polygon onto itself. [b]Standard:[/b] HSG-CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Table of Contents
- Square
- Square
- Regular Pentagon
- Regular Pentagon
- Regular Hexagon
- Regular Hexagon
- 5-Point Star
- 5-Point Star
- Rectangle
- Rectangle
- Isosceles Trapezoid
- Isosceles Trapezoid
- Parallelogram
- Parallelogram
Square
Instructions:
Below, you will find a square HIJK centered at the origin (0,0). [br][br]✔️ Use the slider (a) to rotate the square between 0 and 360 degrees.[br]✔️ Use the check boxes to explore the line(s) of reflection of the pre-image square.
Specify the lines of symmetry for square HIJK
What is the minimum angle of rotation to map square HIJK onto itself?
Select all of the angles of rotation that will map square HIJK onto itself.
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.
Regular Pentagon
Instructions:
Below, you will find a regular (equilateral and equiangular) pentagon. [br][br]✔️ Use the slider (a) to rotate the regular pentagon between 0 and 360 degrees.[br]✔️ Use the check boxes and sliders (α and β) to explore the line(s) of reflection of the pre-image pentagon.
Specify a line of reflection (symmetry) for the pre-image regular pentagon.
What is the minimum angle of rotation that will map the regular pentagon onto itself?
Select all of the angles of rotation that will map the regular pentagon onto itself.
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.
Regular Hexagon
Below, you will find a regular (equilateral and equiangular) hexagon. [br][br]✔️ Use the slider (a) to rotate the regular hexagon between 0 and 360 degrees.[br]✔️ Use the check boxes and sliders (α and β) to explore the line(s) of reflection of the pre-image hexagon.
Specify the line(s) of reflection (symmetry) that will map the pre-image regular hexagon onto itself.
What is the minimum angle of rotation that will map the regular hexagon onto itself?
Select all of the angles of rotation that will map the regular hexagon onto itself.
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.
5-Point Star
Instructions:
Below, you will find a 5-point star.[br][br]✔️ Use the slider (a) to rotate the star between 0 and 360 degrees.[br]✔️ Use the check boxes and sliders (α and β) to explore the star's line(s) of reflection.
Specify a line of reflection (symmetry) that will carry the 5-sided star onto itself.
What is the minimum angle of rotation that will map the 5-sided star onto itself?
Which of the following are angles of rotation that will map the 5-sided star onto itself?
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.
Rectangle
Instructions:
Below, you will find a rectangle centered at the origin (0,0). [br][br]✔️ Use the slider (a) to rotate the rectangle between 0 and 360 degrees.[br]✔️ Use the check boxes and sliders (m, b, α, and β) to explore the line(s) of reflection of the pre-image rectangle.
Specify the lines of reflection (symmetry) for the rectangle.
What is the minimum angle of rotation to map the rectangle onto itself?
Select all of the angles of rotation that will map the rectangle onto itself.
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.
Isosceles Trapezoid
Instructions:
Below, you will find an isosceles trapezoid centered at the origin (0,0). [br][br]✔️ Use the slider (a) to rotate the trapezoid between 0 and 360 degrees.[br]✔️ Use the check boxes and sliders (m, b, α, and β) to explore the line(s) of reflection of the pre-image trapezoid.
Specify the lines of reflection (symmetry) for the trapezoid.
What is the minimum angle of rotation to map the trapezoid onto itself?
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.
Parallelogram
Instructions:
Below, you will find a parallelogram centered at the origin (0,0). [br][br]✔️ Use the slider (a) to rotate the parallelogram between 0 and 360 degrees.[br]✔️ Use the check boxes and sliders (m, b, α, and β) to explore the line(s) of reflection of the pre-image parallelogram.
Specify a line of reflection (symmetry) for the pre-image parallelogram
What is the minimum angle of rotation to map the parallelogram onto itself?
Select all of the angles of rotation that will map the pre-image parallelogram onto itself.
Which of the choices below describe the type of types of symmetry this figure has?
Explain your reasoning:
Write at least 5 sentences explaining your answers.