PROOFS WITH PERPENDICULAR BISECTORS AND MIDSEGMENTS
NAME:__________________________________
1) Where is the circumcenter of
a) an acute triangle?
b) a right triangle?
c) an obtuse triangle?
2) What is true about at least one perpendicular bisector of an isosceles triangle that is not true of
perpendicular bisectors in scalene triangles?
3) Explain the difference between a point of concurrency and a circumcenter.
4) Prove the Perpendicular Bisector Theorem.
5) Prove the Converse of the Perpendicular Bisector Theorem.
6) Prove the Concurrency of Perpendicular Bisectors of a Triangle Theorem.
7) Use a coordinate proof to prove that the circumcenter of a right triangle is located at the
midpoint of the hypotenuse.
8) Prove that, if a perpendicular bisector intersects a vertex of the triangle, the triangle must be
isosceles.
9) Prove that, if a triangle is isosceles, at least one perpendicular bisector must intersect a vertex of
the triangle.
10) Use a coordinate proof to prove the “HL” Theorem.
11) Draw a triangle and its three midsegments. Prove that the four smaller triangles formed are
congruent to each other.