Download 3.1 Day 1 Special Segments and Centers of Triangles .notebook

3.1 Day 1 Special Segments and Centers of Triangles .notebook
3.1 Special Segments and Centers of Triangles
September 30, 2015
Classifications of Triangles:
By Side:
1. Equilateral: three congruent sides
I CAN...
Classify triangles by sides and angles
2. Isosceles: at least two congruent sides
Define and recognize perpendicular bisectors and angle bisectors
3. Scalene: no sides are congruent
Define and recognize points of concurrency.
Jul 24­9:36 AM
Jul 24­9:36 AM
Classifications of Triangles:
By Angle 1. Acute: three acute angles
2. Obtuse: one obtuse angle Point of Concurrency
When three or more lines intersect at the same point
3. Right: one right angle
4. Equiangular: three congruent angles
Jul 24­9:36 AM
A Perpendicular Bisector is a segment or line that passes through the midpoint of a side and is perpendicular to that side.
ED is a perpendicular
bisector of ∆ABC
Jul 24­9:36 AM
The point of concurrency of the perpendicular bisectors is called the circumcenter.
Point A is the circumcenter of the triangle
Jul 24­9:36 AM
Jul 24­9:36 AM
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3.1 Day 1 Special Segments and Centers of Triangles .notebook
Circumcenter Properties
1. The circumcenter is the center of the circumscribed circle.
September 30, 2015
An angle bisector is a segment that divides an angle into two congruent angles. BD is an angle bisector.
m∠ABD= m∠DBC
2. The circumcenter is equidistant to each vertex of the triangle
Jul 24­9:36 AM
The point of concurrency of the angle bisectors is called the incenter.
Point A is the incenter of the triangle
Jul 24­9:36 AM
Incenter Properties
1. The incenter is the center of the inscribed circle
2. The incenter is equidistant to each side of the triangle.
Jul 24­9:36 AM
Jul 24­9:36 AM
DE is a perpendicular bisector of ∆ABC. Solve for x, AE, and AB
D
Solve for x, m∠ABD and m∠ABC Jul 31­9:01 AM
Jul 31­9:01 AM
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