Students test three side lengths or three angles and decide: one triangle, more than one, or none? Eight problems build the triangle inequality by hand. The compass construction stays hidden until students commit a verdict, so reasoning comes before the picture. Covers 7.G.A.2 with a built-in answer key. Includes the degenerate case most worksheets skip. Grade 7, about 20 minutes.
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.
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
What's included
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
This activity develops students' understanding of 7.G.A.2: constructing triangles from three given measurements and determining whether those conditions produce exactly one triangle, more than one, or none. Across eight problems, four with side lengths and four with angle measures, students apply the triangle inequality by hand before committing to a verdict. Because the compass construction stays hidden until they commit, students must reason from the arithmetic rather than the picture. By the end, they can explain why three side lengths fix both shape and size, producing a unique triangle or nothing, while three angles fix only shape, leaving size free.
Draw (freehand, with ruler and protractor, and with technology) 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.
All 7.G.A.2 activities →More interactive, auto-graded activities on the same standards and topics.
Celebrate the holidays with this real-world geometry challenge! Students calculate perimeter, area, and surface area as they decorate a roofline with lights, wrap a wall, design a tree skirt, wrap gift boxes, and paint a festive banner. Perfect for practicing 7th-grade geometry with a fun Christmas theme!
Students use a floor plan on a coordinate grid to measure room dimensions, calculate perimeter, and estimate the total length and cost of baseboard trim needed for an apartment renovation. A hands-on geometry application!
City Intersections is an interactive, auto-graded worksheet for 7th grade geometry (7.G.B.5). Students act as city surveyors, using vertical, adjacent, complementary, and supplementary angles to check whether street crossings meet the road-safety code. They compute the angles, then deliver a verdict: approve or flag. Every student gets a randomized version, so no two worksheets are the same.
In this real-world geometry activity, students calculate area, volume, and circumference of different landscape features to estimate the total cost of a backyard project. Shapes include rectangles, triangles, trapezoids, circles, and more. A perfect blend of math and practical application!
Step into the role of a construction engineer! In this hands-on geometry lab, students estimate costs for concrete, flooring, painting, HVAC, roofing, landscaping, and more using real-world floor plans. Covers area, volume, surface area, and unit conversions. Auto-graded and perfect for 7th grade classrooms.
In this interactive geometry activity, students measure features on a scale map, convert to real-world dimensions, then rescale the layout for a presentation. Visual feedback confirms correct answers instantly. A hands-on way to apply proportional reasoning and scaling!
