Constructions
Lessons in this chapter
About Constructions
Constructions moves geometry from calculating to building, teaching kids to draw a triangle that exactly matches a given set of side or angle measurements using only a compass and straightedge.
Construct triangles using only sides or angles covers two cases: building a triangle from three given side lengths (SSS), and building one from three given angle measures (AAA) — with the chapter making clear that AAA only guarantees the triangle’s shape, not its exact size, since infinitely many similar triangles share the same three angles.
Construct triangles using a combination of side and angle measures covers the mixed cases — two sides and the angle between them (SAS), or two angles and the side between them (ASA) — each producing exactly one possible triangle, which is what makes these combinations reliable ways to construct (and later, to prove triangles congruent).
Frequently asked questions
A compass (for marking off exact, equal distances) and a straightedge or ruler (for drawing straight lines) — no measuring angles freehand and no guessing distances. Construct Triangles Using Only Sides or Angles has kids build precision into every step instead of eyeballing it.
SSS means ‘side-side-side’ — given three side lengths, construct a triangle by drawing one side, then using the compass to mark off the other two side lengths as arcs from each endpoint, and connecting where those arcs intersect to form the third vertex.
SAS means ‘side-angle-side’ — given two side lengths and the exact angle between them, construct one side, use a compass or angle measure to set the given angle at one endpoint, then measure off the second side length along that angle to locate the third vertex.
ASA means ‘angle-side-angle’ — given two angle measures and the length of the side between them, draw that side first, then construct each given angle at its endpoint; the point where the two angle lines cross is the third vertex.
Three angles only fix a triangle’s shape, not its size — a small triangle and a much larger one can share the exact same three angle measures (they’re similar, not identical), so AAA alone can’t pin down one specific triangle the way SSS, SAS, and ASA do. Construct Triangles Using Only Sides or Angles makes this distinction explicit.
Letting the compass width slip while marking an arc, which throws off the side length it’s supposed to represent — the compass has to stay locked at the same width from when it’s set to when the arc is drawn. Checking the final construction’s measurements against the original given values catches this kind of drift.