Angles of Triangles

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Objective

SWBAT prove theorems about the measures of angles of a triangles.

Big Idea

Students will use paper triangles to perform informal proofs about the sum of the interior angles and exterior angles of triangles.

Do Now

7 minutes

As the students enter the room, they are given a paper triangle. I cut the triangles out before the lesson using a thin paper like Origami paper and a paper cutter to make the sides more exact. Students will use their triangles to investigate the sum of the angles by tearing off two angles and reassembling them next to the third angle. I show the students what to do or I project the Angles of Triangles Do Now Instructions.

I circulate while the students work to ensure they put the angles together correctly. Students often put a torn side next to a straight edge.  To help prevent this, instruct the students not to tear their angles neatly when they tear them. 

  

Mini-Lesson

10 minutes

At the beginning of the Mini-Lesson, I ask the students, “What can the activity from the Do Now tell us about triangles?” Students can see that when the angles were laid next to each other, they formed a straight line. Using what students know about the measure of the line, they can see that the sum of the measures of the interior angles in a triangle is 180o.

We then look at another theorem that can be demonstrated by the activity. The sum of the measures of the remote interior angles in a triangle is equal to the measure of the exterior angle. I show the students the presentation, which illustrates the two theorems (G.CO.10). 

Activity

23 minutes

In the Angles of a Triangle Activity students write proofs involving theorems about the angles of a triangle. The first two problems show proofs of the two theorems from the Mini-Lesson. The third problem can be used as a challenge problem. It is a proof showing the sum of the measures of the exterior angles of a triangle.

Students work in groups to complete their proofs. Some students may choose to work on the proofs on their own. Students who find writing proofs challenging are given a list of statements in the order needed to prove the statement. Their task is to match a list of reasons to the statements. Before I give the students the statements and reasons, I cut them out so the reasons are not in the correct order.

Each table has between three and five students. Group roles: cutting out the reasons, pasting the statements on the chart paper, drawing the diagrams, and timekeeper. Students then work together to decide which statements go with which reasons.

Students who complete their proofs before the time ends, can begin to work on the third proof.

 

Summary

5 minutes

At the end of today's proof activity, students hang their chart paper on the wall so that all of the proofs are visible. I plan to call on two students to present their proofs. One student from each group stands by their chart and checks their group’s work. As a class, we will discuss the proofs and the theorems that can be proven from the proofs (MP3). To bring the lesson to closure, I plan to ask my students to write a summary of the proofs on their sheets.