1. Bisectors of a Triangle
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

2. 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

3. 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

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

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

6. 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

7. 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.

8. 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 ?

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