Geometry Vocab From Chapter 5

Front 1

Perpendicular Bisector

Back 1

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint

Front 2

Equidistant from Two Points

Back 2

The same distance from one line as from another point

Front 3

Perpendicular Bisector Theorem

Back 3

If a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

Front 4

Converse of the Perpendicular Bisector Theorem

Back 4

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

Front 5

Distance from a Point to a Line

Back 5

The length of the perpendicular segment from the point to a line

Front 6

Equidistant from the Two Lines

Back 6

The same distance from one line as from another line

Front 7

Angle Bisector Theorem

Back 7

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

Front 8

Converse of the Angle Bisector Theorem

Back 8

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

Front 9

Perpendicular Bisector of a Triangle

Back 9

A line, ray, or segment that is perpendicular to a side of a triangle at the midpoint of the side

Front 10

Concurrent Lines

Back 10

Three or more lines that intersect in the same point

Front 11

Point of Concurrency

Back 11

The point of intersection of concurrent lines

Front 12

Circumcenter of the Triangle

Back 12

The point of concurrency of the perpendicular bisectors of a triangle

Front 13

Concurrency of Perpendicular Bisectors of a Triangle

Back 13

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle

Front 14

Angle Bisector of a Triangle

Back 14

A bisector of a an angle of the triangle

Front 15

Incenter of the Triangle

Back 15

The point of concurrency of the angle bisectors of a triangle

Front 16

Concurrency of Angle Bisector of a Triangle

Back 16

The angle bisectorsof a triangle intersect at a point that is equidistant from the sides of the triangle

Front 17

Median of a Triangle

Back 17

A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side

Front 18

Centroid of the Triangle

Back 18

The point of concurrency of the medians of a triangle

Front 19

Concurrency of Medians of a Triangle

Back 19

The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side

Front 20

Altitude of a Triangle

Back 20

The perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side

Front 21

Orthocenter of the Triangle

Back 21

The point of concurrency of the lines containing the altitudes of a triangle

Front 22

Concurrency of Altitudes of a Triangle

Back 22

The lines containing the altitudes of a triangle are concurrent

Front 23

Midsegment of a Triangle

Back 23

A segment that connects the midpoints of two sides of a triangle

Front 24

Midesegment Theorem

Back 24

The segment connecting the midpoints of two sides of a triangle is parrallel to the third side and is half as long

Front 25

Theorem 5.10

Back 25

If one 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

Front 26

Theorem 5.11

Back 26

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle

Front 27

Exterior Angle Inequality

Back 27

The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles

Front 28

Triangle Inequality

Back 28

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Front 29

Indirect Proof

Back 29

A proof in which you prove that a statement is true by first assuming that its opposite is true. If this assumption leads to an impossibility, then you have proved that the original statement is true

Front 30

Hinge Theorem

Back 30

If two side of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer then the third side

Front 31

Converse of the Hinge Theorem

Back 31

If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the second, then the included angle of the second