Download 5 Minute Check, 26 Sep

Geometry CP, Nov 26
Bisectors of Triangles
Book Section: 5-1
Essential Question: What do you get when you bisect sides and angles
of triangles?
Standards: CCSS G.CO.10, G.MG.3
Perpendicular Bisector
• A bisector is any segment, line, or plane that
intersects a segment at its midpoint.
• A perpendicular bisector is a bisector that is also
perpendicular to the segment.
Examples
Perpendicular Bisector Theorems
Example 1
A. Find BC.
Use the Perpendicular Bisector Theorems
Example 1
Use the Perpendicular Bisector Theorems
B. Find XY.
More Definitions
• Concurrent Lines – Three or more lines that
intersect at a common point.
• Point of Concurrency – The point at which
concurrent lines intersect.
• Circumcenter – The point of concurrency of the
perpendicular bisectors of the sides of a triangle
Circumcenter Theorem
Oh where, oh where can he be?
• The circumcenter can be on the interior, exterior,
or side of a triangle.
Example 2
Use the Circumcenter
Theorem
GARDEN A triangular-shaped garden is shown. Can a
fountain be placed at the circumcenter and still be inside
the garden?
Example 2
Use the Circumcenter
Theorem
Copy ΔXYZ, and use a ruler and protractor to draw the
perpendicular bisectors. The location for the fountain is
C, the circumcenter of ΔXYZ, which lies in the exterior of
the triangle.
C
Answer: No, the circumcenter of an obtuse triangle is in the
exterior of the triangle.
Another Definition
• Angle bisector – A line or plane that divides an
angle into two equal parts.
Angle Bisector Theorems
Example 3
Use the Angle Bisector Theorems
A. Find DB.
Example 3
Use the Angle Bisector Theorems
B. Find mWYZ.
Examples
Last Definition Today
• Incenter (of a triangle) – The point of
concurrency of the angle bisectors of a triangle.
Incenter Theorem
Example 4
Use the Incenter Theorem
A. Find ST if S is the incenter of
ΔMNP.
Example 4
Use the Incenter Theorem
B. Find mSPU if S is the incenter
of ΔMNP.
Examples
Classwork: Textbook p.329, 9-13; p.330,
21, 22, 23, 24, 27-30
Homework: HW Due 11/28, 1-