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ZingPath: Triangles and Their Parts

Interior and Exterior Angles of a Triangle

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Triangles and Their Parts

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Interior and Exterior Angles of a Triangle

Geometry

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

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Now You Know

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.

Everything You'll Have Covered

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.

Tutorial Details

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