Perpendicular Bisectors of a Triangle Activity—Notes
Objectives:
• Students will locate circumcenter of a triangle
• Students will discover that the circumcenter is equidistant from the vertices
of the triangle
• Students will find measures of segments given a triangle with the
perpendicular bisectors drawn in
• Students will discover the location of the circumcenter based on the
classification of the triangle by angle
Prior Knowledge:
• Students must know the classifications of a triangle by angle; acute, obtuse,
and right.
• Students must be familiar with the terms: perpendicular, bisector and
midpoint
• Students need to know and apply the Pythagorean Theorem.
• Students need to know how to simplify radicals.
Perpendicular Bisectors of a Triangle
Definition: Perpendicular Bisector—The perpendicular bisector of a triangle is
a line (or ray or segment) that is perpendicular to the side of a triangle at the
midpoint of the side.
Definition: Circumscribe—To draw a circle around a polygon such that all
vertices of the polygon lie on the circle.
Definition: Concurrent Lines—three or more lines (or segments or rays) that
intersect in the same point. That point is called the point of concurrency
Definition: Circumcenter of a Triangle—The circumcenter of a triangle is the
point of concurrency of the perpendicular bisectors of the sides of a triangle.
Problems:
The perpendicular bisectors of ∆ABC meet at
point D.
a. Find DB
b. Find AE
c. Find ED (Hint: Use the Pythagorean
Theorem.) Write your answer in simplified
radical form.
R is the circumcenter of ∆OPQ. OS = 10,
QR = 12, and PQ = 22.
a. Find OP
b. Find RP
c. Find OR
d. Find TP
e. Find RT