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24 Cards in this Set
- Front
- Back
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Perpendicular Bisector Theorem
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If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
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Converse of the Perpendicular Bisector Theorem
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If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
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Angle Bisector Theorem
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If a point is on the bisector of an angle, then it is equidistant from the two sides of a triangle.
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Converse of the Angle Bisector Theorem
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If a point is in the interior of an angle and is equidistant form the sides of the angle, then it lies on the bisector of the angle.
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concurrent lines
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when 3+ lines intersect in the same point
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point of concurrency
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where 3+ concurrent lines intersect
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circumcenter
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the point of concurrency of the perpendicular bisectors of a triangle
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The circumcenter is _________ inside the triangle.
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Sometimes.
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Concurrency of Perpendicular Bisectors of a Triangle
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The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
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incenter
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point of concurrency of the angle bisectors
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Concurrency of Angle Bisectors of a Triangle
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The angle bisectors The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
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median
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a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
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centroid
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point of concurrency of the medians
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Concurrency of Medians of a Triangle
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The medians of a triangle intersect at a point that is 2/3 of the distance from each vertex to the midpoint of the opposite side.
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altitude of a triangle
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the perpendicular segment from a vertex to the opposite side or line that contains the opposite side
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An altitude is ______________ inside the triangle.
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Sometimes.
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orthocenter
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point of concurrency of the altitudes
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Concurrency of Altitudes of a Triangle
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The lines containing the altitudes of a triangle are concurrent
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midsegment
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segment that connects the midpoints of two sides of a triangle
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Midsegment Theorem
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The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
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Theorem 5.10
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If 1 side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
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Theorem 5.11
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If 1 angle of a triangle is larger than another, then the side opposite the larger angle is longer than the side opposite the smaller angle.
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Extertior Angle Inequality Theorem
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The measure of an exterior angle of a triangle is greater than the measure of erither of the two nonadjacent sides.
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Triangle Inequality Theorem
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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