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Triangle Properties - Pearson Geometry Common Core Chapter 5

Terms in this set (27)

Midsegment of a Triangle
A segment connecting the midpoints of two sides of a triangle. (5.1)
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long. (5.1)
Equidistant
The same distance from two objects. (5.2)
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. (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. (5.2)
Distance from a Point to a Line
The length of the perpendicular segment from the point to the line. This distance is also the length of the shortest segment from the point to the line. (5.2)
Angle Bisector Theorem
If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. (5.2)
Converse of the Angle Bisector Theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector. (5.2)
Concurrent
When three or more lines intersect at one point. (5.3)
Point of Concurrency
The point at which three or more lines intersect. (5.3)
Concurrency of Perpendicular Bisectors Theorem
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. (5.3)
Circumcenter of a Triangle
The point of concurrency of the perpendicular bisectors of a triangle. (5.3)
Circumscribed About
A circle is circumscribed about a polygon if the vertices of the polygon are on the circle. A polygon is circumscribed about a circle if all the sides of the polygon are tangent to the circle. (5.3)
Concurrency of Angle Bisectors Theorem
The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle. (5.3)
Incenter of a Triangle
The point of concurrency of the angle bisectors of a triangle. (5.3)
Inscribed In
A circle is inscribed in a polygon if the sides of the polygon are tangent to the circle. A polygon is inscribed in a circle if the vertices of the polygon are on the circle. (5.3)
Median of a Triangle
A segment whose endpoints are a vertex and the midpoint of the opposite side. (5.4)
Concurrency of Medians Theorem
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. (5.4)
Centroid of a Triangle
The point of concurrency of the medians of a triangle.

Center of gravity of a triangle. (5.4)
Altitude of a Triangle
The perpendicular segment from a vertex of the triangle to the line containing the opposite side. An altitude of a triangle can be inside or outside the triangle, or it can be a side of the triangle. (5.4)
Orthocenter of a Triangle
The point of concurrency of the altitudes of a triangle. (5.4)
Theorem 5-9
The lines that contain the altitudes of a triangle are concurrent. (5.4)
Theorem 5-10
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. (5.6)
Theorem 5-11
If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. (5.6)
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (5.7)
The Hinge Theorem (SAS Inequality 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 opposite the larger included angle. (5.7)
Converse of the Hinge Theorem (SSS Inequality)
If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side. (5.7)
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