Complete symmetric figures

A line-symmetric figure has two matching halves on opposite sides of a line of symmetry: corresponding points are the same perpendicular distance from the line, and the reflected half preserves lengths and shape while reversing orientation. Learners can determine missing parts of simple figures on square grids by reflecting vertices and segments across a horizontal, vertical, or diagonal line; formal coordinate rules, rotational symmetry, and more complex transformations are not included.

Detailed Explanation: Complete symmetric figures

A line of symmetry splits a figure into two matching halves. To complete the missing half:

Look at each corner, or vertex, of the given half.
Count how many squares the vertex is from the symmetry line.
Put the matching vertex the same number of squares on the other side.
Keep the vertex on the same row for a vertical line or the same column for a horizontal line.
Connect the matching vertices.

Example

The vertical line is the line of symmetry. The left half is a triangle.

      1   2   3   4   5   6   7
row 1   .   .   B   |   .   .   .
row 2   .   A   .   |   .   .   .
row 3   .   .   .   |   .   .   .
row 4   .   C   .   |   .   .   .

Complete the triangle on the right.

Vertex $B$ is 1 square left of the line. Place $B'$ 1 square right of the line, on the same row.
Vertex $A$ is 2 squares left of the line. Place $A'$ 2 squares right of the line, on the same row.
Vertex $C$ is 1 square left of the line. Place $C'$ 1 square right of the line, on the same row.

The completed grid looks like this:

      1   2   3   4   5   6   7
row 1   .   .   B   |   B'  .   .
row 2   .   A   .   |   .   A'  .
row 3   .   .   .   |   .   .   .
row 4   .   C   .   |   C'  .   .

Now connect $A'$ , $B'$ , and $C'$ in the same way the original points were connected. The two triangles will have the same size and shape, like mirror images.

Learn by doing: Complete symmetric figures

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2D Shape Symmetry - Which Shape Is Symmetric

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