- Construct the perpendicular bisector of a line segment.
- Apply the Perpendicular Bisector Theorem to identify the point of concurrency of the perpendicular bisectors
of the sides (the circumcenter). - Use the Perpendicular Bisector Theorem to solve problems involving the circumcenter of triangles.
II.Cross-curricular-Origami
- There are several different origami designs that you can do that require the use of an equilateral triangle.
- First, use this website to help the students move from a circle to an equilateral triangle.
- http://www.cyffredin.co.uk/The equilateral triangle.htm
- This will help the students to have an equilateral triangle in design.
- Then you can move on to folding in perpendicular bisectors of the triangle.
- This will help you to identify and mark the circumcenter.
- After the exploration is complete, you can ask the students what they have learned about the perpendicular
bisectors of a triangle and the circumcenter of the triangle. - Brainstorm a list of conclusions on the board.
III.TechnologyIntegration
- Complete a websearch on origami.
- There are several different sites and patterns that students can explore.
- Ask them to select patterns that begin with an equilateral triangle.
- Use this pattern and the equilateral triangle to fold a dolphin or another animal of choice.
- Allow students time to share their work.
IV.NotesonAssessment
- Assessment is completed through observation.
- You can walk around and see students working with the equilateral triangles and the perpendicular bisectors
as they fold their designs.
Angle Bisectors in Triangles
I.SectionObjectives
- Construct the bisector of an angle.
- Apply the Angle Bisector Theorem to identify the point of concurrency of the perpendicular bisectors of the
sides (the incenter). - Use the Angle Bisector Theorem to solve problems involving the incenter of triangles.
II.Cross-curricular-Art
- This activity builds on the origami that the students completed in the last lesson.
- This time, students aren’t going to be working with equilateral triangles but with three different sized triangles.
- Ask the students to cut out triangles that are three different sizes.
- Then with each triangle, students are to fold the paper to show the three bisecting lines of each of the angles
of the triangle. - In the end, the students will have the point of concurrency.
- From there, they can inscribe the circle into the triangle.
Chapter 3. Geometry TE - Enrichment