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Lines of Symmetry

  • Grade 4
  • Mathematics
  • 4.G.A.3
  • Geometry
  • Free lesson

Aligned to 4.G.A.3 — Common Core State Standards for Mathematics.

What this lesson teaches

A line of symmetry is a fold line: if you fold a shape along it, both halves match exactly. Some shapes have no line of symmetry, some have one, and some have many.

Worked examples

Example 1

Take a square. Fold it straight down the middle and the two halves match, so that is a line of symmetry. You can also fold it across, and along both diagonals. A square has 4 lines of symmetry in all.

Example 2

A capital letter A has 1 line of symmetry, straight down the middle. A capital H has 2 — down and across.

Example 3

A parallelogram that is not a rectangle has no lines of symmetry at all, even though it looks balanced. Fold it any way and the halves do not match.

Practice questions

  1. How many lines of symmetry does a rectangle (not a square) have?
  2. Draw a triangle with all equal sides and show its lines of symmetry.
  3. Is the letter H symmetric? Draw any lines of symmetry it has.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Ejes de simetría

Un eje de simetría es una línea de doblez: si doblas una figura por ella, las dos mitades coinciden exactamente. Algunas figuras no tienen ningún eje de simetría, otras tienen uno y otras tienen muchos.

Ejemplo 1: Toma un cuadrado. Dóblalo justo por la mitad y las dos mitades coinciden, así que ese es un eje de simetría. También puedes doblarlo de lado y por las dos diagonales. Un cuadrado tiene 4 ejes de simetría en total.

Ejemplo 2: La letra mayúscula A tiene 1 eje de simetría, justo por el centro. La H mayúscula tiene 2 — vertical y horizontal.

Ejemplo 3: Un paralelogramo que no es rectángulo no tiene ningún eje de simetría, aunque se vea equilibrado. Dóblalo como sea y las mitades no coinciden.

More Geometry lessons

Angles, Lines, and Symmetry4.G.A.1Sorting Shapes by Lines and Angles4.G.A.2

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