Perpendicular Bisectors Theorem

A circumcenter is the point at which three _____________ intersect in a triangle.

• Medians

• Altitudes

• Perpendicular Bisectors

• Angle Bisectors

Use the Perp Bisector Theorem to find DC

• 4

• 1

• 2

• 3

Define: CIRCUMCENTER OF A TRAINGLE

• the intersection point of the three perpendicular bisectors of a triangle 

• when a circle passes through the three vertices of a triangle 

• the point of intersection of three or more lines 

• the intersection point of the three angle bisectors of a triangle 

Point P is the circumcenter, which segment is equal to PB

• DA

• AC

• PC

• PF

If line m is the perpendicular bisector of segment AB, find the value of x.

• x = 8

• x = - 8

• x = 16

• x = - 16

Use the figure and the given information to find the indicated measure. ZX​ is the perpendicular bisector of  WY​, WZ=4n−13​ , and  YZ=n+17​ .

• 27

• 54

• 7

• 13

If CB is a perpendicular bisector, find the value of x.

Use the Perp Bisector Theorem to DC (hint...find x first and then plug it back in to DC)

Mathematical Equivalence

ON

• 12

• 11.5

• 23

• 6

If ZT is a perpendicular bisector, what conclusions can be made?

Answer explanation

If ZT is a perpendicular bisector, then XT is perpendicular to ZT and XT is congruent to YT.