Key to Geometry, Book 7: Perpendiculars and Parallels, Chords and Tangents, Circles

Key to Geometry takes an approach almost no other program uses: students learn geometry by drawing it. Armed with a compass and straightedge, they work through constructions one small step at a time, and the definitions and relationships emerge from what they have built rather than from a block of text they were asked to memorize. Book 7 covers perpendiculars and parallels, then moves into chords, tangents, and the properties of circles — the material where most students first meet genuinely non-obvious results.

The series is a long-standing favorite among homeschoolers for two specific situations. The first is the student who is not ready for a formal proof-based high-school course but needs real geometry content in middle school; the workbooks build the vocabulary and the visual intuition that make a later course far less intimidating. The second is the student who has been beaten up by arithmetic and believes they are bad at math. Because the pages are mostly drawing and because each step is small enough to succeed at, Key to Geometry tends to rebuild confidence quickly. Parents repeatedly describe it as the program that made a discouraged child willing to try again.

Format matters here. These are thin, consumable, non-reproducible workbooks, so each child needs their own copy, and a family working through the whole series will buy all eight. There is no instruction on video and no software; the book is the course. Answers live in separate answer-key booklets covering several books at a time, which is a real cost to plan for. The trade-off for that simplicity is genuine independence — most students can work a page or two a day with almost no parent involvement. Book 7 assumes the constructions from the earlier books, so it is not a sensible starting point on its own; begin at Book 1 unless your student already has the compass work behind them.