Exploring the concept of perpendicular bisectors, this overview delves into their geometric properties, theorems like the Perpendicular Bisector Theorem, and points of concurrency such as the circumcenter and incenter in triangles. It also covers the centroid and orthocenter, highlighting their significance in triangle geometry and practical applications in solving geometric problems.
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1
On a Cartesian plane, the midpoint M of a segment with ends A(x₁, y₁) and B(x₂, y₂) is calculated as M = ((______ + )/2, ( + ______)/2).
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2
Slopes of Perpendicular Lines Relationship
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3
Finding Midpoint of Line Segment AB
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4
Calculating Slope of Perpendicular Bisector
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5
The ______ of the Perpendicular Bisector Theorem asserts that if a point has equal distances from a segment's ends, it is on the segment's bisector.
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6
Circumcenter properties
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7
Incenter properties
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8
Constructing the circumcenter
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9
Depending on the triangle's shape, the ______ can be located inside, on the ______ for right triangles, or outside for obtuse ones.
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10
Perpendicular Bisector Theorem
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11
Angle Bisector Theorem
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12
Median of a Triangle
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