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22 Cards in this Set

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  • Back
perpendicular bisector
…of a side of a triangle is a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side.

Property:
Any point on a perpendicular bisector is equidistant from two vertices
concurrent lines
three or more lines intersecting at a common point
point of concurrency
the point of intersection of concurrent lines
circumcenter
the point of concurrency of the perpendicular bisectors of a triangle
Circumcenter Theorem
The circumcenter of a triangle is equidistant from the vertices of the triangles.
angle bisectors
Property:
Any point on the angle bisector is equidistant from the sides of the triangle.
incenter
the point of concurrency of the angle bisectors of a triangle
Incenter Theorem
The incenter of a triangle is equidistant from each side of the triangle.
median
segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite it
centroid
the point of concurrency of the medians of a triangle
Centroid Theorem
The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.
altitude
...of a triangle is a segment from a vertex through the line containing the opposite side and is perpendicular to that side
orthocenter
the point of concurrency of the altitudes of the triangle
Exterior Angle Inequality Theorem
If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its remote interior angles.
If one side of a triangle is longer than another side, then…
...the angle opposite the longer side has a greater measure than the angle opposite the shorter side
If one angle of a triangle has a greater measure than another angle, then…
...the side opposite the greater angle is longer than the side opposite the smaller angle.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
shortest distance from a point
to a line is…
shortest distance from a point
to a plane is…
SAS Inequality Theorem
(Hinge Theorem)
SSS Inequality Theorem