Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A line of symmetry is a line across a figure such that folding along it makes the two halves match exactly. A heart has one line of symmetry down its middle, a rectangle that is not a square has two, a square has four and a circle has infinitely many. Some figures, like a parallelogram that is not a rectangle or the letter Z, have none at all.
Fourth graders identify line-symmetric figures and draw their lines of symmetry. Folding paper cutouts is the most convincing test: if the edges line up perfectly, the fold is a line of symmetry. A mirror placed along the line gives the same check. Students often discover surprising results, such as a rectangle's diagonal not being a line of symmetry even though it cuts the rectangle into two identical triangles. Those triangles do not land on each other when folded along the diagonal. Symmetry appears in letters, flags, logos and nature, giving plenty of real examples to explore.
Students draw a rectangle's diagonals as lines of symmetry. Folding a paper rectangle along a diagonal shows the corners do not match.
A parallelogram can be cut into two identical halves, but they do not match when folded. Symmetry requires the halves to be mirror images across the line.
Some students look only for vertical lines of symmetry. The letter B has a horizontal line of symmetry and a square has diagonal ones.
How many lines of symmetry does a regular hexagon have, and where are they?
Answer: A regular hexagon has 6 lines of symmetry: 3 through opposite vertices and 3 through the midpoints of opposite sides.
Let students fold paper shapes, letters and pattern block tracings, marking each fold that works. Recording results in a table (shape, number of lines) helps them notice that a regular polygon has as many lines of symmetry as it has sides.
On tests, students are often asked to choose the figure with exactly one line of symmetry or to draw the missing half of a symmetric figure on a grid. Grid practice, counting squares from the line, is ideal preparation.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 4 (also accepted: four)
A square has 2 lines through the midpoints of opposite sides and 2 along its diagonals, for 4 in all.
Answer: C) A
A has a single vertical line of symmetry. H has two, and Z and N have none.
Answer: D) No, folding along it does not make the halves match
The two triangles are the same size, but folding along the diagonal does not line up the corners, so it is not a line of symmetry.
Answer: 3 (also accepted: three)
Each line goes from a vertex to the midpoint of the opposite side, and there are 3 vertices.
Answer: B) Parallelogram with no right angles
A slanted parallelogram does not match itself when folded along any line. The others all have at least one line of symmetry.
A full lesson with slides, activities and an exit ticket on lines of symmetry, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 4.G.A.3 with an answer key, ready in about a minute.
Make a worksheet βTurn lines of symmetry into a quiz students answer online that marks itself, with a class summary for you.
Build a test βFold the shape along the line. If the two halves match exactly, it is a line of symmetry. A small mirror placed on the line gives the same check.
No. Fourth grade focuses on line (reflection) symmetry. Rotations and reflections as transformations are studied in eighth grade under 8.G.A.1.