- Students need to complete this with all three triangles.
- Allow time for the students to share their work in small groups when finished.
III.TechnologyIntegration
- Students can use the following website to explore bisecting angles.
- http://www.geom.uiuc.edu/ demo5337/Group2/incenter.html
- When finished, ask the students to share what they discovered about angle bisectors and inscribing circles.
- Write the conclusions on the board.
IV.NotesonAssessment
- Walk around and observe the students as they work on the paper folding.
- Assist students who are having difficulty.
- Students should see this as a hands- on way to work through the point of concurrency and inscribing circles.
Medians in Triangles
I.SectionObjectives
- Construct the medians of a triangle.
- Apply the Concurrency of Medians Theorem to identify the point of concurrency of the medians of the triangle
(the centroid). - Use the Concurrency of Medians Theorem to solve problems involving the centroid of triangles.
II.Cross-curricular-Art
- Use the concept of Napolean’s Theorem to create a new design/stained glass window effect.
- Review Napolean’s Theorem and how it works.
- Then have students begin to work on a design.
- Students can explore trying different sizes of triangles.
- They can also see if it makes sense to integrate different shapes.
- Since the goal is a stained glass window of sorts, students are going to create a frame and then place different
colored tissue paper inside the frame. - Students can complete this and hang them in the window and the sunlight will come through the design.
III.TechnologyIntegration
- One of the ways to integrate technology into this lesson is to have the students look at some of the other
designs of Napolean’s Theorem. - They can begin by googling Napolean’s Theorem.
- There will be several different websites that will come up where students can read about Napoleans Theorem
and see different patterns and designs. - When finished, students will have expanded their thinking on this theorem.
IV.NotesonAssessment
- Walk around and assist students as they work.
- When finished, assess student designs.
3.5. Relationships Within Triangles