CCSS.Math.Content.8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Does the sum of interior angles change? Why or why not?

This task builds in the understanding of the sum of angles in a triangle, the angle measure of a line, and the interior angle sum of polygons. This activity creates repeated reasoning as it has students build on what they learn in throughout this task. Students discover that the interior angles of a triangle form a line, thus sum to 180 degrees. Next, the task challenges students to put together triangles to form new polygons. This expansion should allows students to then see how a quadrilateral has two triangles with 180 degrees in each, therefore the quadrilateral would have an interior angle sum of 360 degrees. This could be extended out by adding triangles to create polygons with more sides. This repetition should allow students to see a connection between the number of sides in a polygon and the number of triangles within.

Within this task I suspect students will struggle to see that the interior angle sum of polygons is easily found by adding each triangle interior angle measure.

As an extension to this task, higher level students could be given quadrilaterals or other larger polygons and asked to create a system for finding interior angle sums of other shapes. For the lower level students, they might be given a step by step picture guide of the process that we are asking them to follow.