Lines of symmetry, polygons | 3rd grade, 4th grade, 5th grade Math - Free Printable

To complete these symmetrical shapes, you need to draw the mirror image of the part that is already there. Imagine the dashed red line is a mirror. You need to draw exactly what you see on the other side, but flipped over.

Here is how to solve each one:

1. Top Left (Vertical Line):
* Look at the blue shape on the left. It looks like half of a blocky letter "E" or a castle tower.
* To finish it, draw the same steps on the right side of the red line.
* Start from the bottom: go right 1 square, up 1 square, right 1 square, up 2 squares, left 1 square, up 1 square, left 1 square, down 1 square, left 1 square, down 2 squares, right 1 square, down 1 square.
* Actually, an easier way is to look at the distance of each corner from the red line. If a point is 1 square away on the left, its partner must be 1 square away on the right.

2. Top Right (Horizontal Line):
* The shape is above the red line. It looks like a stepped pyramid or stairs going up and then down.
* Draw the reflection below the red line.
* For every point in the top shape, count how many squares up it is from the red line. Then, draw a point the same number of squares *down* from the red line. Connect them in the same order.

3. Middle Left (Vertical Line):
* This shape looks like half of a zig-zag or a lightning bolt.
* Reflect each point across the vertical red line.
* The top point is 2 squares left of the line → draw a point 2 squares right of the line.
* The next point is on the line → stay on the line.
* The next point is 2 squares left → draw 2 squares right.
* Continue this pattern for all corners.

4. Middle Right (Horizontal Line):
* This shape looks like a crown or mountains above the red line.
* Reflect it downward.
* Take each peak and valley of the crown. Count how many squares up they are from the red dashed line. Mark those same distances below the line. Connect the dots to make an upside-down crown.

5. Bottom Left (Vertical Line):
* This is a wavy curve on the left.
* Mirror it to the right.
* Where the wave goes out to the left, your new line should go out to the right by the same amount.
* Where the wave touches the red line, your line also touches the red line.
* It will look like a sideways "S" or a worm when finished.

6. Bottom Right (Horizontal Line):
* This shape has a straight diagonal part and a curved part above the red line.
* Reflect both parts below the line.
* The straight diagonal line goes from the red line up and to the right. Your reflection should go from the red line *down* and to the right at the same angle.
* The curved part bulges upward. Your reflection should bulge *downward* with the exact same curve shape.

Key Tip: Use your grid! Count the squares from the red line to each corner or bend in the shape. Then, count the same number of squares on the other side to place your new points.

Final Answer:
The completed symmetrical shapes are drawn by reflecting the existing blue lines across the red dashed axis. Each half should be a perfect mirror image of the other. Specifically:
- Top-left: A symmetrical blocky "H"-like or castle shape.
- Top-right: A symmetrical hexagon-like shape with flat top and bottom.
- Middle-left: A symmetrical zig-zag diamond or bowtie shape.
- Middle-right: A symmetrical star or double-crown shape.
- Bottom-left: A symmetrical S-shaped curve.
- Bottom-right: A symmetrical leaf or eye shape with pointed ends and curved sides.