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Lines of Symmetry

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 26 of 61.

A shape has a line of symmetry when folding along that line makes the two halves land exactly on each other. Reflecting the shape in the line leaves it looking the same.

$A kite with its one line of symmetry through two corners$

This kite folds along the line through K and M: L lands on N, and the sides KL and KN match. It has only that one line. A rectangle that is not a square has two lines of symmetry, through the midpoints of opposite sides. Its diagonals are not lines of symmetry: fold it along a diagonal and the corners miss each other.

On the board, tap two points, each a corner or the middle of a side, to draw a line through them. Draw every line you find.

Challenge

ABCD is a trapezoid with AB parallel to DC and its two slanted sides equal. Draw every line of symmetry, then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image Image Coordinates The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels

3Rotations

Turning About a Point The Half Turn Quarter-Turn Rules A Center Off the Origin Recap: Rotations

6Symmetry

Lines of SymmetryRotational Symmetry Regular Polygons Symmetry Is a Move Recap: Symmetry

9Bisectors

The Perpendicular Bisector The Midpoint Bisecting an Angle Half of 60°Recap: Bisectors

12Final Challenges

Final: Footprints Final: Two Moves, One Rule Final: Mirror on the Grid Final: The Fair Well Final: The Tangent Road