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3.1 Special Segments and Centers of Classifications of : Triangles By Side: 1. Equilateral: A with three I CAN... congruent sides. Define and recognize bisectors, bisectors, medians, 2. Isosceles: A triangle with at least and altitudes. two congruent sides. 3. Scalene: A triangle with three sides Define and recognize points of having different . (no sides are concurrency. congruent)

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Classifications of Triangles: Special Segments and Centers in Triangles

By angle A Perpendicular Bisector is a segment or 1. Acute: A triangle with three acute that passes through the of a side and . is perpendicular to that side. 2. Obtuse: A triangle with one obtuse angle. 3. Right: A triangle with one 4. Equiangular: A triangle with three congruent angles

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Point of Concurrency The three perpendicular bisectors of a triangle intersect at a single . Two lines intersect at a point. The point of When three or more lines intersect at the concurrency of the same point, it is called a "Point of perpendicular Concurrency." bisectors is called the circumcenter.

Jul 24­9:36 AM Jul 24­9:36 AM 1 Circumcenter Properties An angle bisector is a segment that divides 1. The circumcenter is an angle into two congruent angles. the center of the circumscribed .

BD is an angle bisector. 2. The circumcenter is equidistant to each of the triangles vertices. m∠ABD= m∠DBC

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The three angle bisectors of a triangle properties intersect at a single point. 1. The incenter is the The point of concurrency of the angle center of the bisectors is called the incenter. inscribed circle

Point A is the incenter of the triangle 2. The incenter is equidistant to each AB = AD = AC side of the triangle.

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An is a segment from a The three altitudes of a triangle are perpendicular to the opposite side concurrent. The point of concurrency is called the orthocenter.

m∠ADB= m∠ADC=90° Point A is the orthocenter of the triangle AD is an altitude of ∆ABC

Jul 24­9:36 AM Jul 24­9:36 AM 2 A is a segment from a vertex The three medians of the triangle are to the midpoint of the opposite side concurrent. The point of concurrency is called the .

AB is a median of ∆ACD Point A is the centroid of the triangle.

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