Triangles To Order

Seventh Grade Poster Problem

In this poster problem, students try to build triangles to particular specifications (specs). The specs can include side lengths, angles, or a combination of both.

Students go on to generalize, and develop an understanding about when they can determine a triangle from partial information and when they cannot.


Scissors, Rulers, Protractors, Scratch paper. Lots of scratch paper.

Learning Objectives:

  • Students construct triangles according to specifications (angle and/or side measures).
  • Students recognize that with three conditions, you can often—but not always—determine a triangle.
  • Students begin to understand the rules for when three conditions determine a triangle.

Common Core State Standards for Mathematics:

Teacher Tune Up:

Using protractors. Many students have little experience using protractors—or with angle measure at all, for that matter. Ultimately, we want students to be able to use a protractor to construct or measure angles up to 180° to the nearest degree. See Triangle Conventions and Mechanics.

The issue of whether two triangles are the same (i.e., congruent). We do not make a big deal about that here, but if it comes up, there are two main ways to look at it, described in Triangles and Constraints. The main point is that two triangles are the same if they have the same size and shape. Another way to say it is that they’re the same if you can cut one triangle out (or make a transparency of it) and move it, turn it, and flip it to match the other exactly.

The Lesson Plan:

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Lesson Plan



Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation.

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