Students will inductively discover the Triangle Sum Theorem and deductively prove it using parallel lines. Students will use the Triangle Sum Theorem to prove the Remote Interior Angles Theorem. They will analyze and solve problems that require applying both theorems that they learned and make a conjecture as to whether they think the universe is "flat", "spherical", or "hyperbolic" and how they could test their conjecture using the Triangle Sum Theorem.
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Triangle Sum Theorem and Exterior Angles Theorem
Download the PoerPoint to get the animations and sound effects by selecting the third icon from the upper left corner (downward arrow coming from a rectangle). You will need Geometer's SketchPad v. 5 to see the Hyperbolic and Elliptical Triangle Theorems. (Unfortunately, the Flash File does not open on this website!)
Source: Jerome Noel, John H. Guyer High School
4.1 Triangle sum Theorem Solved