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Exploring Characteristics of Triangles

 Activity Description Activity Guide Resources

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 intangles.gsp.

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