Triangle Builder: One, Many, or None?

Triangle Builder: One, Many, or None? | 7.G.A.2 Triangle Inequality and Angle Sum

Most triangle inequality worksheets let students look at a picture and guess. This one does not. Students do the arithmetic first, commit to a verdict, and only then does the compass construction reveal whether they were right.

What students do

Across eight problems, students work with kits of three measurements and decide whether those conditions determine exactly one triangle, more than one, or no triangle at all.

• Part 1 (4 problems): three side lengths. Students add each pair and compare against the third side, applying the triangle inequality by hand.
• Part 2 (4 problems): three angle measures. Students sum the angles and compare with 180 degrees, discovering that angles fix a triangle's shape but not its size.

After committing a verdict, the construction draws: arcs meeting cleanly for a valid triangle, falling short with the gap measured, or collapsing flat in the degenerate case.

Why this worksheet is different

• Commit before you look. The picture never answers for students. It confirms or corrects their reasoning, which is exactly the "noticing" the standard asks for.
• Includes the degenerate case. One kit has two shorter sides summing to exactly the longest. Students who memorized "greater than or equal to" get it wrong, and the construction shows them why. Most worksheets skip this entirely.
• Both halves of the standard. 7.G.A.2 covers three angles and three sides. Part 1 honestly produces only "one" or "none," since side lengths that close always close in one shape. Part 2 supplies the missing "more than one" case.
• Interactive constructions. Each problem includes a kit view and a verdict view, so students see the compass work rather than a static answer diagram.

What's included

• 8 problems with full worked answers
• Complete answer key
• Teacher guide with common misconceptions and discussion prompts
• Written wrap-up question for assessment

Standards alignment

CCSS.MATH.CONTENT.7.G.A.2: Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Best for

Grade 7 geometry units, triangle inequality introduction or review, angle sum practice, sub plans, math centers, and test prep. Also works as remediation for grade 8 students who need the triangle inequality before Pythagorean theorem work.

Time required: About 20 minutes

Keywords: triangle inequality theorem, 7.G.A.2, triangle angle sum, constructing triangles, unique triangle, geometry worksheet, seventh grade math, middle school geometry, angle sum theorem, triangle construction