Perpendicular Bisectors in Triangles
I.SectionObjectives
- 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.ProblemSolvingActivity-TheCampingDilemma
- Here is the problem.
- “Boy Scout Troop 462 is going on a camping trip. When they arrive at the campground, they are given a huge
triangular field to set up in. The boys decide to place their tents along the perimeter of the triangle and to put
the campfire in the center of the triangle. To do this, they will need to use perpendicular bisectors to identify
the circumcenter.” - Your task is to use the following diagram to help the boy scouts. Draw in the perpendicular bisectors and label
the place where the campfire should go. - Figure05.02.01
- Students can work individually or in pairs on this problem.
- Allow students time to share their work when they are finished.
III.MeetingObjectives
- Students will construct perpendicular bisectors of line segments.
- Students will use the Perpendicular Bisector Theorem to identify the circumcenter of the triangles.
- Students will solve problems by helping the boy scouts with their campfire location.
IV.NotesonAssessment
- Did the students draw in all of the perpendicular bisectors accurately?
- Is the circumcenter in the correct location?
- Did the students identify where the campfire should be?
- Are students able to verbalize how they went about solving the problem?
- Offer feedback and support as students are working.
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.ProblemSolvingActivity-InscribingCircles
- This activity will focus on the students inscribing circles into already designed triangles.
5.5. Relationships within Triangles