Key to Geometry, Book 4: Perpendiculars

Book 4 of the Key to Geometry series concentrates on perpendiculars: dropping a perpendicular from a point to a line, erecting one at a point on a line, bisecting segments and angles, and the constructions that follow from those. Like the rest of the series it is taught entirely through drawing. The student is given a compass and a straightedge, walked through a construction in small numbered steps, and then asked to repeat it under slightly different conditions until the underlying relationship is obvious without anyone having stated it as a rule.

This is the volume where the series starts to feel like real geometry rather than careful tracing, and it is a good place to judge whether the approach suits your student. Children who like building things and dislike reading dense explanations usually take to it. Children who want to know the rule up front and then apply it sometimes find the discovery pacing slow, and for those students a conventional text may be the better spend. The workbook assumes the basic compass handling taught in Books 1 through 3, so it is not a starting point.

The practical appeal is the price. At a few dollars a volume this is close to the least expensive way to put real geometry content in front of a middle-schooler, and for a family testing whether a child is ready for geometry at all, one book is a very cheap experiment. The usual caveats for the series apply: the books are consumable and not reproducible, so siblings each need a copy, and the answer keys are sold separately in booklets that span several volumes. There is no teacher instruction beyond the page itself, which is a feature if you want independent work and a limitation if your student needs someone to explain. Expect roughly a few weeks of short daily sessions to finish it.