Geometry Vocab

Front 1

3 undefined terms in geometry

Back 1

point, line, plane

Front 2

space

Back 2

set of all points

Front 3

collinear

Back 3

a set of points is collinear if there is a line that contains all the points of that set.

Front 4

coplanar

Back 4

a set of points is coplanar if they are all contained in the same plane.

Front 5

Distance Postulate

Back 5

to every two different points, there corresponds a unique positive number.

Front 6

Ruler Postulate

Back 6

the points on a line can be set up in correspondence with the real numbers in such a manner that the distance between any two pointsis equal to the absolute value of the difference between the coordinates of the two points.

Front 7

Betweeness of points

Back 7

For one point to be between two other points all 3 must be different points on the same line.

Front 8

Segment Addition Postulate

Back 8

If B is between A and C, then AB+BC=AC

Front 9

Line Postulate

Back 9

For every two different points there is exactly one line that contains both points.

Front 10

Segment

Back 10

For any two points X and O the segment joining X and O is the union of X and O and all points between X and O.

Front 11

Ray

Back 11

Let A and B be two points. The ray AB is the union of AB and all points C such that B is between A and C

Front 12

Opposite Rays

Back 12

If A is between B and C, then AB and Ac are opposite rays. Opposite rays form a line.

Front 13

midpoint

Back 13

U is the midpoint of FN if U is between F and N and UF=UN

Front 14

Bisector of a segment

Back 14

Any line, segment, ray or plane that intersects a segment at its midpoint. (A bisector splits something into two equal or congruent parts.

Front 15

Angle

Back 15

The union of two non-collinear rays with a common endpoint.

Front 16

Angle Measurement Postulate

Back 16

To every angle there corresponds a measure between 0 and 180 degrees.

Front 17

Angle Addition Postulate

Back 17

If H is in the interior of angle TAM the m of angle HAT + m of angle HAM= m of angle TAM.

Front 18

Linear Pair

Back 18

If EL and EG are opposite rays and EY is any other ray, then angle YEL and angle GEy form a linear pair.

Front 19

Adjacent Angles

Back 19

Two angles are adjacent if they share a common vertex and a common side, but share no common interior points.

Front 20

Supplementary Angles

Back 20

If the sum of two angle's measures = 180 degrees then the two angles are supplementary.

Front 21

Linear Pair Postulate

Back 21

If two angles form a linear pair, then they are supplementary.

Front 22

Congruent Angles

Back 22

Two (or more) angles are congruent if they have the same measure

Front 23

Angle Bisector

Back 23

If D is in the interior of angle ABC and angle ABD is congruent to angle DBC, then ray BD is the bisector of angle ABC

Front 24

Plane Postulate

Back 24

Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane

Front 25

Flat plane Postulate

Back 25

If two points are in a plane, then the line that contains the points is also in that plane.

Front 26

Intersection of Planes Postulate

Back 26

If two planes intersect, then their intersection is a line.

Front 27

Intersection of Lines Theorem

Back 27

If two lines intersect, then they intersect at exactly one point.

Front 28

Midpoint Theorem

Back 28

If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB

Front 29

Angle Bisector Theorem

Back 29

If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC

Front 30

Complementary Angles

Back 30

If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.

Front 31

Right Angle

Back 31

An angle whose measure is 90 degrees.

Front 32

Acute Angle

Back 32

An angle whose measure is less than 90 degrees.

Front 33

Obtuse Angle

Back 33

An angle whose measure is greater than 90 degrees and less than 180 degrees.

Front 34

Vertical Angles

Back 34

Two angles are vertical angles if their sides form two pairs of opposite rays.

Front 35

Vertical Angle Theorem

Back 35

Vertical angles are congruent.

Front 36

Complement Theorem

Back 36

Complements of Congruent Angles are congruent.

Front 37

Exterior sides adjacent angles theorem

Back 37

If the exterior sides of adjacent angles are perpendicular then the angles are complementary.

Front 38

Right Angle Theorem

Back 38

If two angles are right angles then they are congruent.

Front 39

Supplementary Right Angle Theorem

Back 39

If two angles are supplementary and congruent, then they are both right angles.

Front 40

Congruent Linear Pair Theorem

Back 40

If the angles in a linear pair are congruent then each is a right angle.

Front 41

Intersection of Planes Postulate

Back 41

If two planes intersect, then their intersection is a line.

Front 42

Intersection of Lines Theorem

Back 42

If two lines intersect, then they intersect at exactly one point.

Front 43

Midpoint Theorem

Back 43

If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB

Front 44

Angle Bisector Theorem

Back 44

If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC

Front 45

Complementary Angles

Back 45

If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.

Front 46

Right Angle

Back 46

An angle whose measure is 90 degrees.

Front 47

Acute Angle

Back 47

An angle whose measure is less than 90 degrees.

Front 48

Obtuse Angle

Back 48

An angle whose measure is greater than 90 degrees and less than 180 degrees.

Front 49

Vertical Angles

Back 49

Two angles are vertical angles if their sides form two pairs of opposite rays.

Front 50

Vertical Angle Theorem

Back 50

Vertical angles are congruent.

Front 51

Complement Theorem

Back 51

Complements of Congruent Angles are congruent.

Front 52

Exterior sides adjacent angles theorem

Back 52

If the exterior sides of adjacent angles are perpendicular then the angles are complementary.

Front 53

Right Angle Theorem

Back 53

If two angles are right angles then they are congruent.

Front 54

Supplementary Right Angle Theorem

Back 54

If two angles are supplementary and congruent, then they are both right angles.

Front 55

Congruent Linear Pair Theorem

Back 55

If the angles in a linear pair are congruent then each is a right angle.

Front 56

Intersection of Planes Postulate

Back 56

If two planes intersect, then their intersection is a line.

Front 57

Intersection of Lines Theorem

Back 57

If two lines intersect, then they intersect at exactly one point.

Front 58

Midpoint Theorem

Back 58

If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB

Front 59

Angle Bisector Theorem

Back 59

If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC

Front 60

Complementary Angles

Back 60

If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.

Front 61

Right Angle

Back 61

An angle whose measure is 90 degrees.

Front 62

Acute Angle

Back 62

An angle whose measure is less than 90 degrees.

Front 63

Obtuse Angle

Back 63

An angle whose measure is greater than 90 degrees and less than 180 degrees.

Front 64

Vertical Angles

Back 64

Two angles are vertical angles if their sides form two pairs of opposite rays.

Front 65

Vertical Angle Theorem

Back 65

Vertical angles are congruent.

Front 66

Complement Theorem

Back 66

Complements of Congruent Angles are congruent.

Front 67

Exterior sides adjacent angles theorem

Back 67

If the exterior sides of adjacent angles are perpendicular then the angles are complementary.

Front 68

Right Angle Theorem

Back 68

If two angles are right angles then they are congruent.

Front 69

Supplementary Right Angle Theorem

Back 69

If two angles are supplementary and congruent, then they are both right angles.

Front 70

Congruent Linear Pair Theorem

Back 70

If the angles in a linear pair are congruent then each is a right angle.

Front 71

Acute complementary theorem

Back 71

If two angles are complementary then both are acute angles.

Front 72

Congruent Triangles

Back 72

Two triangles are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent.

Front 73

SSS Postulate

Back 73

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front 74

SAS Postulate

Back 74

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front 75

ASA Postulate

Back 75

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front 76

CPCTC

Back 76

C orresponding P arts of C ongruent T riangles are C ongruent.

Front 77

Triangle

Back 77

If A,B and C are 3 non-collinear points, then the union of segment AB, segment BC and segment AC forms a triangle.

Front 78

Scalene Triangle

Back 78

A triangle with no congruent sides.

Front 79

Isosceles Triangle

Back 79

A triangle with two congruent sides.

Front 80

Equilateral Triangle

Back 80

A triangle with all sides congruent.

Front 81

Isosceles Triangle Theorem (I.T.T.)

Back 81

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Front 82

Converse Isosceles Triangle Theorem (C.I.T.T.)

Back 82

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Front 83

Median

Back 83

the median of a triangle is a segment from a vertexto a midpoint of the opposite side.

Front 84

Altitude

Back 84

An altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side.