Symmetry
Site: | Saylor Academy |
Course: | GKT101: General Knowledge for Teachers – Math |
Book: | Symmetry |
Printed by: | Guest user |
Date: | Tuesday, 20 May 2025, 8:13 AM |
Description
Symmetry is an intuitive concept, but in geometry, it has a formal definition. Watch this lecture series and complete the interactive exercises.
Intro to reflective symmetry
Source: Khan Academy, https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-transformation-properties-and-proofs This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
Intro to rotational symmetry
Finding a quadrilateral from its symmetries
Finding a quadrilateral from its symmetries (example 2)
Practice
Reflective symmetry of 2D shapes - Questions
1. The following diagram shows a kite.
Symmetry | Applies to the figure? |
Reflective symmetry over \(y=x\) | Yes/No |
Reflective symmetry over \(y=-x-5\) | Yes/No |
2. Which of the following reflective symmetries apply to the trapezoid below?
Symmetry | Applies to the figure? |
Reflective symmetry over \(\overline{B F}\) | Yes/No |
Reflective symmetry over \(\overline{D H}\) | Yes/No |
3. The center of the following rhombus is at the origin.

Which of the following reflective symmetries apply to the rhombus?
Symmetry | Applies to the figure? |
Reflective symmetry over the line \(y=-2 x\) | Yes/No |
Reflective symmetry over the line \(y=\frac{1}{2} x\) | Yes/No |
4. Which of the following reflective symmetries apply to the hexagon below?
Symmetry | Applies to the figure? |
Reflective symmetry over \(\overline{A D}\) | Yes/No |
Reflective symmetry over \(\overline{C E}\) | Yes/No |
Reflective symmetry of 2D shapes - Answers
1. The symmetries that apply to the kite are:
Symmetry | Applies to the figure? |
Reflective symmetry over the line \(y=x\) | Yes/No |
Reflection symmetry over the line \(y=-x-5\) | Yes/No |
2. The symmetries that apply to the trapezoid are:
Symmetry | Applies to the figure? |
Reflective symmetry over \(\overline{B F}\) | Yes/No |
Reflective symmetry over \(\overline{D H}\) | Yes/No |
3. The symmetries that apply to the rhombus are:
Symmetry | Applies to the figure? |
Reflective symmetry over the line \(y=-2 x\) | Yes/No |
Reflective symmetry over the line \(y=\frac{1}{2} x\) | Yes/No |
4. The symmetries that apply to the hexagon are:
Symmetry | Applies to the figure? |
Reflective symmetry over \(\overline{A D}\) | Yes/No |
Reflective symmetry over \(\overline{C E}\) | Yes/No |
Rotational symmetry of 2D shapes - Questions
1. Which of the following are magnitudes for rotational symmetry of the quadrilateral below about the marked point?
Choose all answers that apply:
(A) \(30^{\circ}\)
(B) \(90^{\circ}\)
(C) \(180^{\circ}\)
(D) None of the above
2. The center of the regular hexagon below is at the origin.
Rotation | Applies to the figure? |
Rotational symmetry of \(60^{\circ}\) about the origin | Yes/No |
Rotational symmetry of \(120^{\circ}\) about the origin | Yes/No |
3. Which of the following are magnitudes for rotational symmetry of the circle below about its center?
Choose all answers that apply:
(A) \(7^{\circ}\)
(B) \(45^{\circ}\)
(C) \(90^{\circ}\)
(D) \(210^{\circ}\)
(E) \(355^{\circ}\)
(F) None of the above
4. The center of the rhombus below is at the origin.

Rotation | Applies to the figure? |
Rotational symmetry of \(90^{\circ}\) about the origin | Yes/No |
Rotational symmetry of \(180^{\circ}\) about the origin | Yes/No |
Rotational symmetry of 2D shapes - Answers
1. The quadrilateral does not have rotational symmetry.
2. This is the completed table:
Rotation | Applies to the figure? |
Rotational symmetry of \(90^{\circ}\) about the origin | Yes/No |
Rotational symmetry of \(180^{\circ}\) about the origin | Yes/No |
3. Of the choices, the circle has rotational symmetry about its center for magnitudes of \(7^{\circ}, 45^{\circ}\), \(90^{\circ}, 210^{\circ}\), and \(355^{\circ}\).
4. This is the completed table:
Rotation | Applies to the figure? |
Rotational symmetry of \(90^{\circ}\) about the origin | Yes/No |
Rotational symmetry of \(180^{\circ}\) about the origin | Yes/No |