Triangle Connections to Supplementary Angles
Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Mathematical Practice #7 Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure.

The idea behind this activity is to help those students who are visual learners make a more concrete connection as well as extend the more advance thinker to the next level of making connections between various concepts such as dealing with adjacent angles and moving towards solving for missing angles.
Teacher Preparation
For a more challenging group of students teacher may consider having triangles already cut out.
For a more diverse or advanced group the teacher may have the students create their own triangles given a classification (without measurements).
Determine if the students should work individually, in pairs, or small groups (3).
Familiarize self with progressions/scope to determine openers as well as the directions to move towards preparing the students for the next level.
Determine how many triangles each pair/group will have and base the movement of the activity or to guide the discussions.
Activating Prior Knowledge
Review classification of triangles. Vocabulary

In this part of the activity teacher can actually have the students discuss the triangles in their groups. Give them about 2 to 3 minutes to talk about the triangle and its properties. The teacher should walk around and make sure the conversations and discussions are authentic. Do not share out to the group since the students will have to share later with another student in the class.
Activity
Have students complete the main activity. Teacher will walk ensuring that students are on task and focused. Also ask questions making sure to call on the student who maybe a little more reserve in the actual activity. Make sure the all the students can elaborate on the two questions and not just give one-word answers. They should be able to discuss why they feel their answer is appropriate and right.
Discussion
When all the angles of a triangle meet at one vertex, will they always form a straight angle?
By having the students not only look at various triangles also have them use the same triangle or as a “I Do, We Do” activity you demonstrate one of the triangles used by students however, cut it up a different way and perform the activity.
As a whole group discuss the classification of the triangles and then show how they are cut up differently. Either show this activity using a computer simulation or using the overhead and having the two triangles next to each other when forming the straight angle.
Will the sum of the measurement of the triangle angles always be supplementary? Why or Why not?
The students should realize that no matter what kind of triangle it is they are going to always create a straight angle when they pull all the angles together.
Prove that the sum of the measurements is 180 degrees. Have students measure (or already have measurements for angles of triangles that used in the exploratory activity). Ask the students how can they solve or prove that the answer is 180 degrees. Have students calculate the sum of the angles.

Based on the various triangles utilized in the exploratory activity, jigsaw your partners with another partner that had a different triangle, have them discuss with their new partner what they found with their activity. Did everyone get the same answer of 180 even though their triangles were different?
Teacher should just be circulating the room, listening and interjecting when needed.
Is it possible to make complementary connection with all three angles why or why not?
The student should say no since complementary means that the sum of the angles equal 90 degrees. The rule is the sum of the 3 angles in a triangle is 180 degrees.
Teacher notes: the idea here was to activate prior knowledge and to build on one concept to prove another. By having students discuss things that they already know it is important for students to be able to talk math with math vocabulary. The vocabulary is not new and they are using other concepts to relate to this particular concept, therefore they are demonstrating Mathematical
Practice 7, which is making use of structure.