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Math
Geometry
Holt Geometry Chapter 5 Vocabulary
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Gravity
Definitions, postulates, and theorems
Terms in this set (27)
equidistant
the same distance from two or more objects
locus
a set of points that satisfies a given condition
Perpendicular Bisector Theorem
If the point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
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
Angle Bisector Theorem
If a point is on the angle bisector of an angle, then it is equidistant from the sides of the angle
Converse of the Angle Bisector Theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the angle bisector of the angle
concurrent
a point where three or more lines intersect at one point
point of concurrency
point where three or more lines coincide
circumcenter of a triangle
the point of concurrency of the three perpendicular bisectors of a triangle
circumscribed circle
every vertex of the polygon lies on the circle
incenter of a triangle
the point of concurrency of the three angle bisectors of a triangle
inscribed circle
a circle in which every side of the polygon is tangent to the circle
Circumcenter Theorem
The circumcenter of the triangle is equidistant from the vertices of the triangle
Incenter Theorem
The incenter of a triangle is equidistant from the sides of the triangle
median of a triangle
a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side
centroid of the triangle
the point of concurrency of the three medians of a triangle
altitude of a triangle
a perpendicular segment from a vertex to the line containing the opposite side
orthocenter of a triangle
the point of concurrency of the three altitudes of a triangle
Centroid Theorem
The centroid of a triangle is located ²/₃ of the distance from each vertex to the midpoint of the opposite side
midsegment of a triangle
a segment that joins the midpoints of two sides of the triangle
Triangle Midsegment Theorem
The midsegment of a triangle is parallel to a side of the triangle, and its length is half of the length of that side
indirect proof
a proof in which the statement to be proved is assumed to be false and a contradiction is shown
Theorem 5-5-1
If two sides of a triangle are not congruent, then the larger angle is opposite the larger side
Theorem 5-5-2
If two angles of a triangle are not congruent, then the larger side is opposite the larger angle
Triangle Inequality Theorem
The sum of any two side lengths of a triangle is greater than the third side length
Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included side
Converse of the Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle and the third sides are not congruent, then the larger included angle is across from the longer third side
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