Completing symmetric figures
Complete a simple symmetric figure with respect to a specific line of symmetry
What a learner can do afterwards
- Given half a butterfly shape and a mirror line, complete the other half on a grid
- Complete a symmetric pattern on squared paper with a vertical line of symmetry
- Check a completed figure by folding along the mirror line
1 · Read
A line of symmetry is a mirror line. If you fold a shape along this line, both halves land exactly on top of each other. You already know how shapes look and how they move on a grid. Now you will use that grid to finish a shape when you only see half of it.
Zara sees half a butterfly wing drawn on squared paper, with a mirror line down the middle. For every square she counts on one side, she counts the same square on the other side, the same distance from the line. She marks a dot there, then joins the dots to finish the wing.
To check your work, fold your paper along the mirror line. If the two halves match up exactly, your drawing is symmetrical. If a part sticks out, fix that part.
A line of symmetry is a mirror line: copy each square the same distance on the other side, then fold to check.
More to read
Symmetry review
A shape is symmetric when one half mirrors the other across a line. Fold along that mirror line and the two halves land exactly on top of each other. Every spot on one side has a twin spot the same distance out on the other side. To finish half a butterfly, copy each mark across the line at the same distance. Count squares from the line to place each twin correctly. Then fold your drawing in your mind to check: twins that line up mean you got it right.
How to Find an Axis of Symmetry: Method, Examples, & More
An axis of symmetry is the fold line that splits a shape into matching halves. Hold a mirror along a candidate line: if the reflection completes the shape, that line is a mirror line. Rectangles have two, squares have four, and many blobs have none. Try each direction one at a time: vertical, then flat, then diagonal. For patterns on squared paper, count squares out from the line on both sides. Equal counts on both sides confirm the mirror. Unequal counts mean that line is not a mirror.
Reflecting shapes
Reflecting copies each point to the other side of the line at the same distance. A point 2 squares left of the line lands 2 squares right of it after the flip. Distance from the line never changes in a mirror image. Near points stay near, far points stay far. Build the copy corner by corner. Measure each corner to the line, then mark its twin the same steps out on the far side. Join the twins and the mirrored shape appears.
Reflections review
The fold test is the judge of symmetry. Fold the finished figure along the mirror line: exact overlap means symmetric, gaps or overhangs mean something is off. One stray dot overlapping empty paper breaks the match. Fix it by moving that dot to its true twin spot. Most classroom patterns use a vertical mirror line down the middle. Left and right swap places while up and down stay the same.
Explore more
2 · Watch
Take it off screen
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.