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Perpendicular and Angle Bisectors of a Triangle Sec 5.2 Goal: To use properties of perpendicular bisectors of a triangle. To use properties of angle bisectors of a triangle.
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Perpendicular Bisectors of an Obtuse Triangle Review: The perpendicular bisector of a triangle is a line that is perpendicular to a side of the triangle at the midpoint of the side. Point of concurrency or circumcenter The three perpendicular bisectors are outside the triangle for an obtuse triangle.
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Obtuse Triangle The perpendicular bisectors of a triangle intersect at a point P that is equidistant from the vertices of the triangle. Theorem 5.5 Point of concurrency or circumcenter PA = PB = PC
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Perpendicular Bisector of an Acute Triangle Point of concurrency or circumcenter The three perpendicular bisectors are inside the triangle for an acute triangle.
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Acute Triangle Point of concurrency or circumcenter PA = PB = PC The perpendicular bisectors of a triangle intersect at a point P that is equidistant from the vertices of the triangle. Theorem 5.5
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Perpendicular Bisector of a Right Triangle Point of concurrency or circumcenter The three perpendicular bisectors are on the triangle for a right triangle.
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Right Triangle Point of concurrency or circumcenter PA = PB = PC The perpendicular bisectors of a triangle intersect at a point P that is equidistant from the vertices of the triangle. Theorem 5.5
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Angle Bisector of a Triangle Angle bisector An angle bisector of a triangle – a line that bisects an angle of the triangle.
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Angle Bisectors of a Triangle The three bisectors are concurrent at a point P called the incenter
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Angle Bisectors of a Triangle The three bisectors are concurrent at a point P called the incenter The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. Theorem 5.6 PD = PE = PF
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Example The perpendicular bisectors met at point P. Find PC. Find DP.
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Example The angle bisectors met at point M. Find MK. Find ZK.
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Example You have three salesmen who are selling cars and you are looking for a location to build a plant to manufacture cars.
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