- Extension- does this continue to prove true if more triangles are added? Where can they be added?
III.MeetingObjectives
- Students will construct the medians of a triangle.
- Students will show how Napoleans Theorem works.
- Students will explain their thinking through a presentation.
- Students will demonstrate understanding through each person’s design.
IV.NotesonAssessment
- Is student work accurate?
- Does it show accurate equilateral triangles?
- Are the students able to explain their work to prove Napolean’s Theorem?
- What happens when the pattern is extended beyond three levels? Are there more equilateral triangles to be
found? - Offer feedback and support as students work.
Altitudes in Triangles
I.SectionObjectives
- Construct the altitude of a triangle.
- Apply the Concurrency of Altitudes Theorem to identify the point of concurrency of the altitudes of the
triangle (the orthocenter). - Use the Concurrency of Altitudes Theorem to solve problems involving the orthocenter of triangles.
II.ProblemSolvingActivity-DrawingTriangles
- In this activity, students are going to demonstrate that they understand the concepts associated with altitude
by constructing different triangles.
- Students need to construct an acute triangle.
- Label the altitude of the triangle.
- Label the orthocenter.
- Students need to construct an obtuse triangle.
- Label the altitude of the triangle.
- Label the orthocenter of the triangle.
- Students need to construct a right triangle.
- Label the altitude of the triangle.
- Label the orthocenter of the triangle.
- Allow students time to share their work in small groups.
III.MeetingObjectives
- Students will construct the altitude of a triangle.
- Students will locate and label the orthocenter of a triangle.
- Students will demonstrate understanding through their constructions.
IV.NotesonAssessment
5.5. Relationships within Triangles