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Identify Line-Symmetric Figures and Draw Lines of Symmetry

Students identify which figures from a set are line-symmetric and which are not, and draw all lines of symmetry on line-symmetric figures. Students also complete a figure given half of it and a line of symmetry.

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Identify Line-Symmetric Figures and Draw Lines of Symmetry

Grade 4 · Line Symmetry · question 1 of 3

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20 rungs. A star at the top.

Find all fold-matches of the pendant and count them.

Count the lines of symmetry.

How it is taught

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A line of symmetry folds a figure onto itself.

Some figures have more than one such fold.

Read it: Fold it so the halves match

Fold this rectangle along line 1 and every corner lands on a matching corner, so line 1 is a line of symmetry.

  1. Try one line at a time, and picture folding the shape along it.
  2. Count the corners on each side of the line.
  3. Call it a line of symmetry only if every corner lands on a matching corner.

A line of symmetry cuts a shape into two halves that are mirror images.

If one side has more corners than the other, the halves cannot match.

Some shapes have several lines of symmetry, and some have none at all.

A line of symmetry folds a shape onto itself, every corner on a matching corner.

Calling the rectangle's diagonal a line of symmetry because it cuts the shape in half.

Fold along the diagonal and the corners miss each other. Equal halves are not enough: they must match when folded.

How many lines of symmetry does a rectangle that is not a square have? — 2. It folds up and down and across, but not along a diagonal: 2 lines.

Find the line of symmetry of a triangle

Today we'll learn about line symmetry. A shape has line symmetry if we can fold it so both halves match exactly.

Look at this triangle. Could we fold it so the two sides line up?

Grade 4 · Folding figures into matching halves

Where would we fold? Try to picture a fold line straight down the middle.

Right here! We draw a line straight down from the top point to the bottom edge.

The left side mirrors the right side. Every point on the left has a matching point on the right.

That fold line is called a line of symmetry. This triangle has exactly one.

But not every shape works. This lopsided triangle has no fold that makes matching halves — it has zero lines of symmetry.

Some shapes have more than one. A rectangle has two lines of symmetry — one vertical and one horizontal.

A line of symmetry splits a figure into two matching halves. To find them, look for every fold that makes the two sides line up perfectly.

Now you try. Count the lines of symmetry. How many symmetry lines?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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