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A Square on a Segment

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 52 of 61.

A square needs four equal sides and a right angle. Each comes from a tool you already have: the Perpendicular gives the right angle, and circles carry the length.

$The square KLMN built on KL$

For a square on KL: draw the line KL, then the perpendicular at L. The circle about L through K marks M on it, so LM = LK. The circles about K through L and about M through L cross at N, so KN = KL and MN = ML. Four equal sides with a right angle at L: KLMN is a square.

Challenge

Construct a square on AB: find its two other corners, then press Check. The Perpendicular tool is unlocked.

Try it yourself

$Construct it with a compass and straightedge$

Construct it with a compass and straightedge

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

2Reflections

Reflecting in a Line The Two Axes The Line y = x Find the Mirror Recap: Reflections

5Dilations

Scaling From a Center Shrinking a Shape Dilating About a Point Negative Scale Factors Recap: Dilations

8Compass and Straightedge

Circles Keep Distances Why the Sides Match Angles You Built A 60° Angle Recap: Equilateral Triangle

11Constructed Shapes

A Square on a SegmentThe Regular Hexagon Copy an Angle A Tangent From a Point Recap: Constructed Shapes