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Symmetry Is a Move

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 28 of 60.

A line of symmetry is a mirror that maps the shape onto itself. The shape lands where it was, but its corners swap places.

$A rectangle PQRS and its upright line of symmetry$

Reflect rectangle PQRS in its upright line of symmetry, x = $\frac{5}{2}$ . P lands where Q was and Q where P was; S and R swap too. The picture looks unchanged, but every corner has moved. A half turn about the center of the rectangle also lands it on itself: then P goes to R and Q to S.

Challenge

Triangle ABC has two equal sides, CA and CB. The dashed target is ABC itself, with A and B swapped: A' must land where B is and B' where A is. Find the mirror that does it, apply it, then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image 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 Symmetry Rotational Symmetry Regular PolygonsSymmetry Is a MoveRecap: 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