Video: Identifying the Figure That Has the Most Lines of Symmetry

Which of the following has the most lines of symmetry? [A] equilateral triangle [B] rectangle [C] square

02:30

Video Transcript

Which of the following has the most lines of symmetry — equilateral triangle, rectangle, or square?

Why don’t we start by sketching each of these shapes? First, an equilateral triangle, a triangle where all three sides are the same length. Next up, rectangle.

To determine which shape has the most lines of symmetry, we’ll need to find out how many lines of symmetry is in each shape. Remember that our lines of symmetry are the places where one-half of our shape is reflected to the other half.

Here’s one place. If you folded the triangle at this line, both halves are equal. Here is another line of symmetry for an equilateral triangle. And finally, a third line of symmetry for equilateral triangles. This equilateral triangle and in fact all equilateral triangles have three lines of symmetry. Next up, the rectangle. We can fold the rectangle in half this way or this way, giving the rectangle two lines of symmetry.

Let’s take a closer look at the square. We know that squares are one type of rectangle. Just like the rectangle, they can be divided in half this way and this way. But there’s something special about squares. They can also be divided in half diagonally. That means the square has the two lines of symmetry that all rectangles have plus two more, each diagonal. All squares have four lines of symmetry. Which of the following has the most lines of symmetry? The square.

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