OBJECTIVE: To identify properties of perpendicular bisectors and angle bisectors BIG IDEAS:Reasoning and Proof Measurement ESSENTIAL UNDERSTANDINGS: A triangle’s three perpendicular bisectors are always concurrent A triangle’s three angle bisectors are always concurrent MATHEMATICAL PRACTICE: Look for and make use of structure

TERMS Concurrent lines:_______________ or more lines that _______________ in the same point Point of Concurrency:the _______________ of _________________________ of concurrent lines Circumcenter of the Triangle:the point of _________________________ of the _________________________ bisectors of a triangle Concurrency of Perpendicular Bisectors of a Triangle Theorem:the ____________________ _______________ of a triangle ____________________ at a point that is ____________________ from the ____________________ of the triangle

Circumcenter of the Circumscribed Triangle The Circumcenter is the center of the circle that passes through the vertices of the triangle. The circle is _________________________ about The Circumcenter of a triangle can be inside, on, or outside a triangle

EXAMPLE EX 1: The perpendicular bisectors of meet at point a) Find A D E b) Find G B F C c) Find

EXAMPLE Ex 2: R is the circumcenter of a) Find O b) Find U S R c) Find Q T P d) Find

TERMS Angle bisector of a triangle:a ___________________ of an angle of the triangle. Incenter of the Triangle:the point of ____________________ of the _______________ bisectors of a triangle. Concurrency of Angle Bisectors of a Triangle Theorem:the ____________ _____________________ of a triangle ____________________ at a point that is _____________________ from the ____________ of the triangle

Incenter of an Inscribed Triangle The Incenter is the center of the circle that touches each side of the triangle once. The circle is __________________ in The Incenter of the triangle is always inside the triangle.

EXAMPLE EX 3: The angle bisectors of meet at point a) Find Y J K b) Find M X L Z c) What is the value of ?

EXAMPLE EX 4: P is the incenter of. Find the value of B S Q P A R C

14 questions