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## 6th grade foundations (Eureka Math/EngageNY)

### Course: 6th grade foundations (Eureka Math/EngageNY)>Unit 3

Lesson 1: Topic A: Foundations

# Intro to reflective symmetry

Introduction to the concept of an "axis of symmetry". Created by Sal Khan.

## Want to join the conversation?

• What does `line of symmetry` mean and how can you apply it to a shape? because i don't understand that at all and what can you not use it on?
• The line of symmetry is the imaginary line where you could fold the image and have both halves match exactly.
• A circle has infinite lines of symmetry right?
• Yes.
Any straight line that passes through the center of a circle is also a line of symmetry of that circle.
• i thought the line of symmetry was where you could fold the image and have both hales match exactly
• You thought right! Some shapes cannot have a line of symmetry, but for those, which can, an imaginary line (sometimes called the axis) runs through the center cutting the figure into two identical parts. Keep in mind, the two parts will often be mirror images, depending on the figure.
• Does the number of sides of the shape change the amount of lines of symmetry?
• It does change, but depends more on if the polygon is regular or not. If a polygon is irregular, chances are there will be less lines of symmetry. An equilateral triangle will have 3 lines of symmetry, but a scalene triangle will have none. If a polygon is regular, the number of sides it has is the amount of symmetry lines it will have.
• can there be a infinite number of lines of symmetry?
(1 vote)
• can rotational symmetry be used in organic shapes?
• yes, organic shapes such as snow flakes can have rotational symmetry.
• Why the line of symmetry in rectangle have only two why not four
• Great question!

A line of symmetry must not only divide the figure into two congruent parts, but also must be perpendicular to every segment that connects a point in one part to the corresponding point in the other part.

While a diagonal divides a rectangle into two congruent triangles, that alone doesn’t necessarily imply that it is a line of symmetry.

Let’s say we have a non-square rectangle ABCD (in counterclockwise order) with diagonal BD. In the two congruent triangles formed, point A must correspond to point C. However, the segment connecting A and C is not perpendicular to diagonal BD. So diagonal BD is not a line of symmetry. For a similar reason, diagonal AC is not a line of symmetry.

Therefore, the two diagonals of a non-square rectangle do not count as lines of symmetry!

Have a blessed, wonderful day!
• what is 721,390 x 635,495