A girl folding colorful paper shapes at a bright craft table

Fold It! Lines of Symmetry

Maya folds paper shapes for her art project. Where can she fold so both halves match perfectly?

4th Grade Math

Step 1: The Fold Test

Maya draws a dashed line down the middle of her square. She imagines folding along that line. What happens to the two halves?

The halves match exactly! A fold line like this is called a line of symmetry. Fold along it, and both parts fit perfectly.

Step 2: Test Another Fold

Next, Maya tests a rectangle with a horizontal dashed line. She wants evidence that the fold works. Is this line a line of symmetry?

Fold the top down onto the bottom. Both halves land exactly on each other, so this horizontal line is a line of symmetry.

Let's Remember

The Fold Test

          Step 1: Draw a line across the figure.

          Step 2: Imagine folding along that line.

          Step 3: If both parts match exactly, it is a line of symmetry.

Analyze every fold with this test. Some figures have many lines of symmetry. Some have none at all!

How Many Lines?

Maya investigates her square and tests every possible fold. Each green dashed line passes the fold test. How many lines of symmetry does a square have?

A square has 4 lines of symmetry: vertical, horizontal, and both diagonals. Every one of those folds makes matching halves.

Watch Out!

The Diagonal Trap

          Fold a rectangle along its diagonal and the corners stick out. The halves do NOT match.
          A rectangle has only 2 lines of symmetry, not 4.
        

Practice: Test the Line

Is the dashed line a line of symmetry for this triangle?

Fold along the dashed line. The left half lands exactly on the right half, so it passes the fold test.

Symmetry in Letters

F B L

Which letter has a horizontal line of symmetry?

B works! Fold B along a middle horizontal line, and the top loop matches the bottom loop. F and L do not match when folded.

Symmetry in an Array

Look at this whole rectangle made of 3 rows and 4 columns. Determine how many lines of symmetry the whole rectangle has.

A vertical middle line works, and a horizontal middle line works. Diagonal folds fail the fold test, so the answer is 2.

Fill in the Blank

A regular hexagon has ? lines of symmetry.

A regular hexagon has 6 lines of symmetry. 3 connect opposite corners, and 3 connect the middles of opposite sides.

Draw the Line

Maya wants to draw the line of symmetry on a paper heart. A heart has exactly 1 line of symmetry. Where should she draw it?

Draw it straight down the middle, from the dip at the top to the point at the bottom. Fold there, and the two bumps match perfectly.

Challenge: The Circle

Maya tests a circle. Every straight line through the center makes matching halves. So how many lines of symmetry does a circle have?

Every line through the center passes the fold test. A circle has countless lines of symmetry, more than anyone could ever draw!

Where do you see symmetry in nature or in your home? How could you use a fold to prove it?

Great Work!

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