Unit Plan 15 (Grade 7 Math): Constructing Triangles & Conditions
7th graders construct triangles from given sides and angles using tools and reasoning. They apply the triangle inequality, analyze SSS, SAS, ASA, AAS, and SSA cases, and determine when conditions create one, multiple, or no possible triangles.
Focus: Draw triangles from given conditions (sides/angles); determine when a set of conditions yields a unique, multiple, or no triangle.
Grade Level: 7
Subject Area: Mathematics (Geometry • Construction & Reasoning)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students learn to construct triangles from conditions and to reason about existence and uniqueness. Using ruler, protractor, and optional compass or dynamic geometry, they build triangles from SSS, SAS, ASA, AAS, and SSA data and decide whether the conditions determine one triangle, more than one triangle, or no triangle. Emphasis: triangle inequality, angle sum 180°, clear construction steps, and written justifications (why one, many, or none).
Essential Questions
- Which sets of measurements guarantee a unique triangle, and why?
- When can the same conditions create two different triangles—or no triangle at all?
- How do the triangle inequality and angle sum guide construction and reasoning?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Interpret and use triangle data (sides/angles) to plan a construction with appropriate tools.
- Construct triangles from SSS and SAS using arcs/circles or precise measurement; argue why the triangle is unique.
- Construct triangles from ASA and AAS with a protractor; argue why the triangle is unique.
- Investigate SSA (side–side–angle, non-included angle) and determine conditions for 0, 1, or 2 triangles; explain using sketches/arcs and the triangle inequality.
- Decide unique / multiple / none for mixed condition sets and justify decisions in writing.
Standards Alignment — CCSS Grade 7
- 7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on triangles given three measures of angles or sides, including cases where no triangle exists or more than one triangle exists.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.5 (use tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can choose tools (ruler, protractor, compass/technology) and follow accurate steps to build the triangle.
- I can use triangle inequality and angle sum 180° to check if a triangle is possible.
- I can explain why SSS, SAS, ASA, AAS give one triangle.
- I can show with a diagram why SSA can give two, one, or zero triangles.
- I can label and write a clear justification for unique / multiple / none.