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Bisectors of a Triangle

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Presentation on theme: "Bisectors of a Triangle"— Presentation transcript:

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


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