Handout 5
Name: ________________________
Ms. Buchanan – Honors Geometry
Lesson 1.12
Date:____________
Geometric Invariants: Sketchpad Exploration
Concurrency in Triangles
1. Use geometry software to draw a triangle. Construct the perpendicular bisector of each side.
Can you adjust the triangle so that the three perpendicular bisectors are not concurrent?
________________________________________________________
2. Hide the perpendicular bisectors. Construct the angle bisectors of your triangle. Can you adjust
the triangle so that the three angle bisectors are not concurrent?
________________________________________________________
3. Under which circumstances, if any, are the three perpendicular bisectors and the three angle
bisectors of a triangle all concurrent?
________________________________________________________
Name: ________________________
Ms. Buchanan – Honors Geometry
Lesson 1.12
Date:____________
Geometric Invariants: Sketchpad Exploration
Concurrency in Triangles
1. Use geometry software to draw a triangle. Construct the perpendicular bisector of each side.
Can you adjust the triangle so that the three perpendicular bisectors are not concurrent?
________________________________________________________
2. Hide the perpendicular bisectors. Construct the angle bisectors of your triangle. Can you adjust
the triangle so that the three angle bisectors are not concurrent?
________________________________________________________
3. Under which circumstances, if any, are the three perpendicular bisectors and the three angle
bisectors of a triangle all concurrent?
________________________________________________________
Handout 5
Concurrency in Pentagons
1. Place five points on your screen. Connect them with segments so that you have an arbitrary
convex pentagon. Construct the perpendicular bisector of each side of your pentagon.
2. Is it possible to adjust the vertices of the pentagon so that at least three bisectors are
concurrent?
________________________________________________________
3. Is it possible to adjust the vertices of the pentagon so that all five bisectors are concurrent?
________________________________________________________
4. Place five new points on your screen. Connect them with segments so that you have another
arbitrary convex pentagon. Construct the angle bisector of each angle of your pentagon.
5. Is it possible to adjust the vertices of the pentagon so that at least three bisectors are
concurrent?
________________________________________________________
6. Is it possible to adjust the vertices of the pentagon so that all five bisectors are concurrent?
Concurrency in Pentagons
1. Place five points on your screen. Connect them with segments so that you have an arbitrary
convex pentagon. Construct the perpendicular bisector of each side of your pentagon.
2. Is it possible to adjust the vertices of the pentagon so that at least three bisectors are
concurrent?
________________________________________________________
3. Is it possible to adjust the vertices of the pentagon so that all five bisectors are concurrent?
________________________________________________________
4. Place five new points on your screen. Connect them with segments so that you have another
arbitrary convex pentagon. Construct the angle bisector of each angle of your pentagon.
5. Is it possible to adjust the vertices of the pentagon so that at least three bisectors are
concurrent?
________________________________________________________
6. Is it possible to adjust the vertices of the pentagon so that all five bisectors are concurrent?