Investigating the Triangle Sum Theorem and Corollary
- Topic:
- Geometry
Move the blue points to create an acute triangle. What is the sum of the interior angles of the triangle?
Move the blue points to create an obtuse triangle. What is the sum of the interior angles now?
Move the blue points once more to create a right triangle. What is the sum of the interior angles now?
Working Toward Proof
The blue lines are parallel to each other. The red lines act as transversals of the parallel lines. What is the relationship between the interior angles of the triangle and the angles formed by the transversals?
Working Toward Proof
Exterior Angle Theorem
An exterior angle of a triangle is the angle between any side of the triangle and a ray extended outward from an adjacent side. In the applet below, the red angle is an exterior angle of the triangle.
What is the sum of and ?
A remote interior angle is an interior angle of a triangle that is not adjacent to a particular exterior angle. In this example, the green and purple are remote interior angles of the red exterior . What is the relationship between the sum of the and and the ?
A remote interior angle is an interior angle of a triangle that is not adjacent to a particular exterior angle. In this example, the purple and teal are remote interior angles of the red exterior . What is the relationship between the sum of the and and the ?