Time for Triangles

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SWBAT identify key types of triangles when given angles and sides, and will prove number of degrees in a triangle.

Big Idea

Students will measure, cut and measure again to learn and prove key properties of triangles

Do Now

10 minutes

Students can work independently on the Do Now questions which asks students to sketch angles like right, acute and obtuse and also requires them to use algebra to solve a triangle perimeter problem.

Exploration #1 and Vocabulary

25 minutes

This lesson centers on 8.G.A.5* as I have found that my students require the review of this content prior to launching into triangle proof topics.  As the CCSS is implemented, this lesson may not be necessary but I will definitely be including it in my curriculum for the next couple of years until students have a stronger prerequisite knowledge of these topics. 

You can introduce students to triangles using the first exploration which asks students to build upon their prior knowledge by creating triangles and measuring angles and sides.  This is a great time to emphasize "equi" as a pre-fix since we see this being used in equilateral and equiangular.  We also can introduce isosceles triangles, and discuss how base angles are congruent (the next lesson, Time for More Triangles, will devel into this topic more fully!). 

After reviewing the topics covered in the exploration with student-led discussion, a Euclid video will review all the key kinds of triangles.  You can show this before or after reviewing the vocab section with students; it helps to break up the 90 minute class. Please note the Euclid video is aimed for a younger population but I find my students really enjoy it, particularly those students who like drawing.  There is also a mistake at the end of the video about obtuse angles/triangles - you can challenge your students to find the mistake.  I would tell my students, "There is a mathematical mistake in this video (near the end), see if you can identify it!" 


NOTE: the complete Student Notes - Time for Triangles handout is included in this section of my lesson.

*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. 

Exploration #2 and Proof of Triangle Sum Theorem

25 minutes


10 minutes

These two examples in the practice section will help students apply the knowledge that they have learned in this lesson.  These examples can be lead by the teacher or done in pairs by students and then reviewed.  Again, these examples may be review for students. 


5 minutes

Students can work on the activity in class, if time remains, or complete this assignment for homework.

Exit Ticket

10 minutes

As an exit ticket students will be asked to find the length of a side using algebra and their newly learned concept of isosceles triangles.  This is a great question because students need to go beyond just solving for x, and also must plug in to find each side length.  You can remind students that after plugging in for x, the two congruent sides should have the same measure - a great self-check!