Video: Lines of Symmetry in Plane Geometry

Does the flag of India have a line of symmetry?

02:14

Video Transcript

Does the flag of India have a line of symmetry?

Like most flags, the flag of India is a rectangle shape. We can see that it’s been split into three equal parts. And these form three stripes. Each stripe is a rectangle by itself. We’ve got an orange rectangle, and then a white rectangle, and at the bottom of the flag we have a green rectangle. And in the very centre of the flag, there is a blue wheel which has 24 spokes. The question asks us whether this shape, this design, has a line of symmetry. A line of symmetry is a line that we can draw down a shape dividing it into half so that both halves are exactly the same.

We can draw a vertical line down the centre of the flag of India. And we can notice several things. The orange rectangle on the left-hand side of the line is the mirror image of the orange rectangle on the right-hand side of the line. The white rectangle on the left-hand side of the line is also exactly the same as the white rectangle on the right-hand side of the line. And the same is true of the green rectangle.

By drawing a line down the centre, we’ve split each of the three stripes exactly in half. Perhaps the part of the flag that we really need to think about is the wheel in the centre. But because a wheel is a circle shape, we can see that this also can be divided into half down a centre. The left side is a mirror image of the right side. In fact, if we folded the flag from the right side all the way over to the left side, it would fold over perfectly. Each of the stripes would fit neatly on each other, and so would the wheel.

It’s a little tricky to draw here, but we could also put a mirror along the line of symmetry. And if we did this, one-half of the flag would reflect perfectly across, and we’d see the whole flag. Does the flag of India have a line of symmetry, a line that divides it perfectly in half with both halves the same? The answer is yes.

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