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HW: pg. 311-312 (1-10)
5.1-5.3 Quiz Friday 12-14-12
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Name _________________________
Geometry CPA
5-2 Bisectors of Triangles
GOAL:
I will be able to:
1. prove and apply properties of perpendicular bisectors of a triangle.
2. prove and apply properties of angle bisectors of a triangle.
Date ________
Part A---PERPENDICULAR BISECTORS
Since a triangle has three sides, it has three perpendicular bisectors. When you construct
the perpendicular bisectors, you find that they have an interesting property.
When three or more lines intersect at one point, the lines are said to be ________________.
The ______________ concurrency is the point where they intersect. In the demonstration,
you saw that the three perpendicular bisectors of a triangle are concurrent. This point of
concurrency is the ____________________ of the triangle.
The circumcenter can be _________, __________, or ____ the triangle as illustrated below.
The circumcenter of ΔABC is the center of its circumscribed circle. A circle that contains all
the vertices of a polygon is _________________ about the polygon.
Example 1: Using Properties of Perpendicular Bisectors
YOU TRY:
Z is the circumcenter of ∆GHJ .
a. Find GM.
b. Find JZ.
Example 2: Finding the Circumcenter of a Triangle
Find the circumcenter of ∆HJK with vertices H(0, 0), J(10, 0), and K(0, 6).
YOU TRY:
Find the circumcenter of ∆GOH with vertices G(0, –9), O(0, 0), and H(8, 0) .
Part B---ANGLE BISECTORS
A triangle has three angles, so it has three angle bisectors. The angle bisectors of a triangle
are also concurrent. This point of concurrency is the _______________ of the triangle.
Unlike the circumcenter, the incenter is always __________ the triangle.
The incenter is the center of the triangle’s inscribed circle. A circle _______________ in a
polygon intersects each line that contains a side of the polygon at exactly one point.
Example 3: Using Properties of Angle Bisectors
Find mPMN.
YOU TRY:
Find mPQX.
5-2 Practice
3. Lee’s job requires him to travel to X, Y, and Z. Draw a sketch to show where he should buy a
home so it is the same distance from all three places.