Adding the Angles in a Triangle

Student Summary

A 180∘180^\circ angle is called a straight angle because when it is made with two rays, they point in opposite directions and form a straight line.

A line with point marked. Angle is marked 180 degrees. 

If we experiment with angles in a triangle, we find that the sum of the measures of the three angles in each triangle is 180∘180^\circ— the same as a straight angle!

Through experimentation we find:

  • If we add the three angles of a triangle physically by cutting them off and lining up the vertices and sides, then the three angles form a straight angle.

  • If we have a line and two rays that form three angles added to make a straight angle, then there is a triangle with these three angles.

    A triangle. The angles are colored blue, red, and green. A line with two rays forming three angles. The angles are colored blue, red, and green.

Visual / Anchor Chart

Standards

Building On
7.G.2

Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Addressing
8.G.2

Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.

8.G.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.