In the previous lesson, students were given collections of triangles and noticed that they shared angle and side measures, and that sometimes there was more than one type of triangle with the same measures. In this lesson and the next, they build on that experience by drawing their own triangles with specified measures: a given angle, two given angles, and two given angles and a given side length. The purpose of the two lessons is to give students experience using various tools to draw triangles with given conditions, and to help them see that sometimes the given conditions allow only one possible triangle, sometimes more than one, and that sometimes none. Note that in grade 7, students are not expected to know that the angles within a triangle sum to \(180^\circ\), although it is fine for them to use that information if they know it.
- Draw triangles with two given angle measures and one side length, and describe (orally) how many different triangles could be drawn with the given conditions.
- Use drawings to justify (in writing) whether two given angle measures and one side length determine one unique triangle.
Let’s see how many different triangles we can draw with certain measurements.
- Given two angle measures and one side length, I can draw different triangles with these measurements or show that these measurements determine one unique triangle or no triangle.