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Cards In This Set
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Perpendicular Bisector
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A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.
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Equidistant from Two Points
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The same distance from one point as from another point.
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Theorem 5.1
Perpendicular Bisector Theorem |
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
If CP is the perpendicular bisector of AB, the CA = CB. |
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Theorem 5.2
Converse of the Perpendicular Bisector Theorem |
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
If DA = DB, the D lies on the perpendicular bisector of AB. |
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Distance from a point to a line
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The length of the perpendicular segment from the point to the line.
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Equidistant from the Two Lines
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The same distance from one line as from another line.
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Theorem 5.3
Angle Bisector Theorem |
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If m BAD = m CAD, then DB = DC. |
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Theorem 5.4
Converse of the Angle Bisector Theorem |
If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.
If DB = DC, then m BAD = m CAD. |
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Section 5.1
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Section 5.2
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Perpendicular Bisector of a Triangle
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A line, ray, or segment that is perpendicular to a side of a triangle at the midpoint of the side.
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Concurrent Lines
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Three or more lines that intersect in the same point.
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Point of Concurrency
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The point of intersection of concurrent lines.
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Circumcenter of the Triangle
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The point of concurrency of the perpendicular bisectores of a triangle.
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Theorem 5.5
Concurrency of Perpendicular Bisectors of a Triangle |
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
PA = PB = PC |
