Perpendicular Bisectors in Triangles
Materials Needed: Patty paper, ruler, protractor, colored pencils
Lesson Opener Activity
1. On a sheet of patty paper, draw and label
.
2. Fold the paper so that A lays directly on top of B. Crease the fold.
3. Open the paper and draw a line on the crease from edge to edge.
4. Label the point of intersection between
and the folded line M.
5. Label a second point anywhere on the creased line as C.
6. Measure
and
. MA = _________ MB = _____________
7. Measure CMA and CMB.
mCMA = ___________ mCMB =
____________
8. Based on your measurements, use correct vocabulary to describe the pair of
intersecting lines on your paper?
______________________________________________________________
9. Draw a segment from C to A, then another segment from C to B.
10. Measure
and
CA = __________________ CB = __________________
11. Label another point on the creased line as D.
12. Repeat steps 9 and 10. DA = _________________ DB = ___________________
13. Based on your observations, make a conjecture about any point on the perpendicular
bisector of a segment.
______________________________________________________________
______________________________________________________________
Materials Needed: Patty paper, ruler, protractor, colored pencils, compass
Group Activity (groups of three or four)
1. One student in the group will draw a large acute triangle, one will draw a large right
triangle, and one will draw a large obtuse triangle on a piece of patty paper. The
fourth student can draw a triangle of his/her choice. Label it ∆ABC.
2. As in the previous activity, fold one side of the triangle to form the perpendicular
bisector of the side (fold your paper so that A lies directly on top of B and crease
the line).
3. Repeat for the other two sides. What do you notice about the three creased lines?
_____________________________________________________________
4. Label the point of intersection of the creased lines D. The point of intersection of
three or more lines is also called the point of concurrency.
5. Using a colored pencil, draw a line on one crease from the side of the triangle to
point D. Repeat for the other two sides. Verify that the lines are perpendicular and
the sides of the triangle are bisected and label the diagram showing this.
6. Using a different colored pencil, draw a dashed line from point D to each vertex of
the triangle.
7. Measure the length from each vertex to point D.
DA = _____________ DB = ___________ DC = ______________
8. Compare your results with the other members of your group. What can you conclude
about the point of intersection of the perpendicular bisectors of a triangle?
______________________________________________________________
______________________________________________________________
How is this conjecture related to the Opening Activity?
______________________________________________________________
9. Compare your triangle with the same type in other groups. Describe the location of
the point of intersection of the perpendicular bisectors on all three triangles.
Acute Triangle _______________________
Right Triangle _______________________
Obtuse Triangle ______________________
Extension Activity
Using a compass, construct a circle with the center at D and the radius the length
of
Compare the circle you constructed with your group members. What do you
notice about the relationship between the triangle and the circle you constructed?
______________________________________________________________
______________________________________________________________
______________________________________________________________
 The point of concurrency of the perpendicular bisectors of a triangle is
called the circumcenter because it is the center of the circle that is
circumscribed about (goes around the outside of) the triangle.