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Parallel Through a Point

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 49 of 61.

To draw the parallel to a line through a point R, build a rhombus. Opposite sides of a rhombus are parallel, so one of its sides on the line gives the parallel through R.

$The rhombus XRWQ, whose side RW is parallel to the line through X and Q$

Take a point X on the line. The circle about X through R crosses the line at Q, so XQ = XR. The circle about R through X and the circle about Q through X cross again at W, so RW = RX and QW = QX. All four sides of XRWQ equal XR: it is a rhombus. RW is opposite XQ, so RW is parallel to the line.

Challenge

Construct the line through P parallel to the line AB, then press Check.

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 PointParallel Through a PointTools You Have Earned Recap: Parallels