Question Video: Identifying Lines of Symmetry in a Circle | Nagwa Question Video: Identifying Lines of Symmetry in a Circle | Nagwa

Question Video: Identifying Lines of Symmetry in a Circle Mathematics • Third Year of Preparatory School

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Which of these are lines of symmetry of the circle?

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Video Transcript

Which of these are lines of symmetry of the circle?

Here, we’re looking for the line of symmetry in the circle or the reflection symmetry of a circle. A line of symmetry or a line of reflection will create a mirror image of that shape. Sometimes, if it’s difficult to visualize a reflection, it can be helpful to trace the shape that we’re trying to reflect and then folding it along the line of reflection.

So let’s look at this line 𝐶 and visualize what would happen if we folded the circle along line 𝐶. This smaller part of the circle would be folded on top of the larger part. However, the piece that we’ve folded over would not lie exactly on top of the remaining piece. This means that line 𝐶 is not a line of symmetry.

Let’s have a look at line 𝐵. So if we imagine we’re folding this part of the circle across the line 𝐵, then the shape would look something like this. Once again, we can see that line 𝐵 is not a line of symmetry.

So now let’s try folding the circle across line 𝐴. In this case, the two halves of the circle would fit exactly on top of one another. In fact, we can say that any line passing through the center of a circle is an axis of symmetry because it divides the circle into two identical parts.

Because there are an infinite number of lines that can pass through the center of a circle, then the circle has an infinite number of lines of symmetry. However, in this question, we were given a choice of three lines, which could be lines of symmetry. And therefore, the answer is that the line of symmetry here is line 𝐴 only.

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