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Geometry

The properties of the interior and exterior angles of triangles are observed.

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After completing this tutorial, you will be able to complete the following:

- Recognize that the sum of the interior angles of a triangle equals 180 degrees.
- Identify equal angles (corresponding and vertical) formed by a triangle with two transversals and a line parallel to the base of the triangle passing through the other vertex.
- Recognize that an exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices.
- Calculate the measurement of an exterior angle using the measurement of the interior angles at the other two vertices.

The sum of the interior angles of a triangle equals 180 degrees.

When the three interior angles of any triangle are added together, they will always equal 180 degrees.

A triangle with two transversals and a line parallel to the base of the triangle passing through the other vertex has several equal angles.

- A triangle with two transversals and a line parallel to the base of the triangle passing through the other vertex has several equal angles.
- corresponding angles - two congruent angles, both lying on the same side of the transversal and situated the same way on two different parallel lines, are equal; angles 3 and 4 are corresponding angles.
- vertical angles - angles that are opposite one another at the intersection of two lines; angles 5 and 6 are vertical angles.

An exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices.

In this drawing, let x be the measure of .

So, to find the measure of the exterior angle, add the interior angles at the other two vertices.

The following key vocabulary terms will be used throughout this Activity Object:

- exterior angles of a triangle - the angles formed by a side of a triangle and an extension of an adjacent side; angle x is an exterior angle of the triangle.
- interior angles of a triangle - the angles formed inside the sides of a triangle; angles b and c are interior angles of the triangle.
- triangle - a polygon with three sides and tree angles.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should know the angles, corresponding angles, interior and exterior angles, triangles, and vertical angles. |

Course | Geometry |

Type of Tutorial | Visual Proof |

Key Vocabulary | angles, exterior angles of a triangle, interior angles of a triangle |