- To prepare the activity, have several triangles drawn out for the students.
- Divide the students into groups.
- Each group needs to receive three different triangles.
- The students are completing these tasks at the same time. Each students completes his/her part of inscribing
the triangle. - The first student draws in one angle bisector and passes the triangle to the right.
- The next student draws in the next angle bisector and passes the triangle to the right.
- The next student draws in the perpendicular bisectors.
- The final student uses a compass to inscribe the circle.
- When finished, the students will have completed this task for three different triangles.
III.MeetingObjectives
- Students will construct the bisectors of angles in a triangle.
- Students will draw in perpendicular bisectors of the angles in a triangle.
- Students will use a compass to inscribe a circle into a triangle.
- Students will share their work with peers.
IV.NotesonAssessment
- Check student work for accuracy.
- Are the angles bisected corrected?
- Are the perpendicular bisectors correct?
- Have the students located the circumcenter?
- Is the circle correctly inscribed into the triangle?
- Can the students explain how and why they completed each piece the way that they did?
- Offer feedback/correction when necessary.
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.ProblemSolvingActivity-Napolean’sTheorem
- Begin by sharing Napolean’s Theorem with the students from the Wikipedia site. Use the diagram as well this
is Figure05.04.01 - http://en.wikipedia.org/wiki/Napoleon%27s_theorem
- Students are going to prove Napoleans Theorem.
- Tell students that they are going to create a design three levels in complexity to prove Napoleans Theorem.
- Show them that the Wikipedia diagram is three levels of complexity.
- Students can use chart paper, colored pencils, and rulers.
- They need to be prepared to show, through their diagram, how Napolean’s Theorem is accurate and true.
- Each student works on his or her own design, but you may want to allow them to work in groups to help each
other.
Chapter 5. Geometry TE - Problem Solving