Isosceles Triangles Forever

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Students will prove that base angles in an isosceles triangle are congruent and will apply their knowledge of isosceles triangles.

Big Idea

Isosceles, who? Isosceles, what? This engaging lesson helps students prove and apply properties of isosceles triangles using colors and highlighters.

Do Now

10 minutes

In this Do Now, students will review properties of equilateral and equiangular triangles.  This will help students to see that for these triangles there is a direct relationship between the measurements of the sides of a triangle and their angle measurements (much like isosceles triangles!).  This Do Now also reviews triangle sum theorem.

Isosceles Triangle Vocabulary, Theorem and Proof - using color

25 minutes

Applied Triangle Problems and Constructions

25 minutes

For the practice problems, students can first try the problems alone and then seek help from each other or the teacher.  I would suggest having students explain their steps to solving for the entire class to discuss and critique (MP3) since there are a lot of important triangle concepts involved in finding each missing angle. 

For the constructions I will often ask students to complete each step of the construction following along with me and the corresponding video, pausing the video at each step to check in with students' progress. For this lesson I two helpful videos, how to construct a scalene triangle  and how to construct an isosceles triangle using a compass and straight-edge (MP5).  Additionally This website provides a step-by-step guide on how to construct an isosceles triangle as well which is great for learners for students who need scaffolded steps.

Practice/Homework and Exit Ticket

15 minutes

Students can work on the applied triangle problems using properties of isosceles triangles in the practice/homework questions.  Students can start the assignment in class, and then finish at home, if you are running short on time. 

There is also a challenging proof problem (MP7) which asks students to prove triangles congruent in a complex diagram.  You can direct students to shade or color in the triangles that we are trying to show congruent in the diagram to help them get started on this proof.  The scaffolded questions will help to further guide students towards a flow proof.  Extra practice with isosceles triangles proofs can be found in assignments in the Overlapping Triangles lesson.

The exit ticket can be handed out after students have had time to work on the practice/homework.  The exit ticket asks students to apply their knowledge of isosceles triangles and angles in a diagram with multiple triangles. 

Triangle Proof Project

5 minutes

By now, students should have handed in their proof to be reviewed and you should be in the process of giving feedback to students.  If there are any technology issues, they should be addressed now as there are only 2-3 days till presentations will be shown in class.  Materials for this project can be found here.