Students draw triangles and explore the classification of each using the measures of interior angles and lengths of sides. In the extension activities, the students further explore and generalize a formula for the sum of the interior angles of convex polygons.

Mathematics:  The students will investigate the sum of the interior angles of various triangles and conjecture and prove the following theorem:

• The sum of the interior angles in a triangle is 180° .

The extension activities include conjecturing and proving the following theorems:

• The sum of the interior angles in a quadrilateral is 360° .

• The sum of the measures of the interior angles in a convex n-gon is 180°(n-2).

Mathematics Thinking: Students will be asked to predict, conjecture, generalize and prove the aforementioned theorems.

Technology:  This activity uses several Sketchpad commands such as: New Sketch, Point tool, Segment, Selection Arrow tool, Text tool, Preferences, Calculate, Length, and Angle measure.

The following sketch illustrates the relationship between the measures of the interior angles in a triangle. The sketchpad file has been saved as angles.gsp.