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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 1 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 2