Grade 5 › G5U09 Geometry: Symmetry

GRADE 5 · ALBERTAOUTCOME AB-G5-5G1.1

L1 · Lines of Symmetry

Learning goal

“I can test a shape for reflection symmetry with the fold test, I can find and count a shape's lines of symmetry, and I can describe where a line of symmetry runs in words. I can also recognize a plane of symmetry in a 3-D shape.”

Reflection symmetry — a shape has it when one half is the mirror image of the other half.
Line of symmetry — the line a shape can be folded on so the two halves match exactly.
Mirror image — the flipped copy of a shape: same size, same shape, facing the opposite way.
Vertex — a corner point of a shape (plural: vertices).
Worked example

Does the letter A have reflection symmetry, and how many lines of symmetry do a square and a rectangle have? Step 1: The test is a fold. Imagine a vertical line down the middle of the letter A and fold along it. The left half lands exactly on the right half - every edge matches, nothing sticks out. So A HAS reflection symmetry, and that fold line is a line of symmetry. Step 2: Run the same test on a square, four ways: vertical fold - match. Horizontal fold - match. Diagonal fold corner to corner - match. Other diagonal - match. A square has 4 lines of symmetry. Step 3: Run it on a rectangle (longer than it is wide). Vertical and horizontal folds match. But fold corner to corner along a diagonal and the edges stick out past each other - the halves do NOT match. A rectangle has only 2 lines of symmetry. Say it plainly: never guess from the shape's name or from having "pairs of equal sides." Run the fold test, one candidate line at a time.

Check yourself — explain it

A shape has reflection symmetry when…

Paired problem — example still visible

Does the letter H have a HORIZONTAL line of symmetry? -> Yes - folding top to bottom makes the halves match, so H has both a vertical and a horizontal line (2 in total).

Faded completion — last step is yours

"Fold an equilateral triangle along the line from one vertex to the middle of the opposite side. The halves match, so that line is a ___" -> line of symmetry (the triangle has 3 such lines in total, one from each vertex)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.