Symmetry

Site: Saylor Academy
Course: GKT101: General Knowledge for Teachers – Math
Book: Symmetry
Printed by: Guest user
Date: Saturday, May 18, 2024, 3:08 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 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.



Which of the following reflective symmetries apply to the 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.


Which of the following rotational symmetries apply to the regular hexagon?

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.



Which of the following rotational symmetries apply to the rhombus?

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