In this lesson, the focus is on the interior angles of a triangle. What can we say about the three interior angles of a triangle? Do they have special properties?
The lesson opens with an optional activity looking at different types of triangles with a particular focus on the angle combinations of specific acute, right, and obtuse triangles. After being given a triangle, students form groups of 3 by identifying two other students with a triangle congruent to their own. After collecting some class data on all the triangles and their angles, they find that the sum of the angle measures in all the triangles turns out to be 180 degrees.
In the next activity, students observe that if a straight angle is decomposed into three angles, it appears that the three angles can be used to create a triangle. Together the activities provide evidence of a close connection between three positive numbers adding up to 180 and having a triangle with those three numbers as angle measures.
A new argument is needed to justify this relationship between three angles making a line and three angles being the angles of a triangle. This is the topic of the following lesson.
- Comprehend that a straight angle can be decomposed into 3 angles to construct a triangle.
- Justify (orally and in writing) that the sum of angles in a triangle is 180 degrees using properties of rigid motions.
Let’s explore angles in triangles.
Print copies of the Tear it Up blackline master. Prepare 1 copy for every group of 4 students. From the geometry toolkit, students will need scissors.
If you are doing the optional Find All Three activity, prepare 1 copy of the Find All Three blackline master for every 15 students. Cut these up ahead of time.
- If I know two of the angle measures in a triangle, I can find the third angle measure.
alternate interior angles
Alternate interior angles are created when two parallel lines are crossed by another line called a transversal. Alternate interior angles are inside the parallel lines and on opposite sides of the transversal.
This diagram shows two pairs of alternate interior angles. Angles \(a\) and \(d\) are one pair and angles \(b\) and \(c\) are another pair.
A straight angle is an angle that forms a straight line. It measures 180 degrees.
A transversal is a line that crosses parallel lines.
This diagram shows a transversal line \(k\) intersecting parallel lines \(m\) and \(\ell\).