Unit 1, Lesson 14
Parallel Lines and the Angles in a Triangle
Accelerated 7
Preparation
Lesson Narrative
In this lesson, students apply properties of rigid transformations to show that the sum of the interior angles of any triangle is .
Students first use rigid transformations to explore the sum of the angles in a triangle drawn on a grid. They rotate the triangle so that angles corresponding to its three interior angles form a straight line. This shows that the three angles sum to . However, this argument depends on the grid lines to show the three angles form a straight angle.
Then students complete the argument without using a grid. Instead, they use the structure of parallel lines cut by a transversal, corresponding parts of congruent triangles, and straight angles to generalize that the sum of the angles in any triangle is (MP7).
In the optional activity, students have additional practice using the same structures to find angle measures in a composite figure.
- Create diagrams using 180-degree rotations of triangles to justify (orally and in writing) that the measure of angles in a triangle sum up to 180 degrees.
- Generalize that the sum of angles in a triangle is 180 degrees using rigid transformations or the congruence of alternate interior angles of parallel lines cut by a transversal.
Let’s see why the angles in a triangle add to 180 degrees.
Required Materials
Activity 2
Required Preparation
None