Geometry Definition, Postulates, And Theorems

Front 1

collinear points

Back 1

points that lie on the same line

Front 2

noncollinear points

Back 2

points that do not lie on the same line

Front 3

Two ________ determine a unique straight line.

Back 3

points

Front 4

________ noncollinear points determine a unique ________.

Back 4

Three, plane

Front 5

A ________ ____________ is a part of a line consisting of two points, called end points, and the set of all points ___________ them.

Back 5

line segment, between

Front 6

Ruler Postulate

Back 6

subtract coordinates of the points and then take the absolute value

Front 7

Betweenness of Points

Back 7

If F, G, and H are collinear and FG and GH equal FH, then G is between F and H. (F-G-H)

Front 8

A ____ is a part of a line consisting of a given point, called the ____ ________, and the set of all points on one side of the end point.

Back 8

ray, end point

Front 9

An _______ is the union of two rays having the same end point.

Back 9

angle

Front 10

The end point of an angle is called the ________.

Back 10

vertex

Front 11

The rays in an angle are called the ______ of the angle.

Back 11

sides

Front 12

Angles that have equal measures are called ___________ ______.

Back 12

congruent angles

Front 13

There is a degree measure for every angle from 0-180 degrees and an angle for every degree measure. What postulate is this?

Back 13

protractor postulate

Front 14

Ray PS is between ray PQ and ray PR; if point S lies in the interior of m< QPR and m<SPR+m<QPS =m<QPR. What definition is this?

Back 14

betweenness of rays

Front 15

A ______ _______ is an angle with a measure of 90 degrees.

Back 15

right angle

Front 16

An angle less than 90 degrees is called an _______ angle.

Back 16

acute

Front 17

An angle that is greater than 90 degrees and less than 180 degrees is called an ________ angle.

Back 17

obtuse

Front 18

The ___________ of a line segment is the point that _______ the line segment into two congruent line segments.

Back 18

midpoint, divides

Front 19

A ___________ of line segment AB is any line, ray, or line segment which passes through the ____________ of line segment AB. What definition is this?

Back 19

bisector, midpoint ; definition of a bisector

Front 20

What definition states that ray OR is the bisector of <PON if R lies in the interior of <PON and m<POR=m<RON?

Back 20

definition of an angle bisector

Front 21

If equals are added to equals, the results are equal. If a=b, then a+c=b+c. What property is this?

Back 21

addition property

Front 22

The ____________ property states that if equals are __________ from equals, then the results are equal: a=b, then a-c=b-c

Back 22

subtraction, subtracted

Front 23

The ____________ property states that if equals are ____________ by equals, their products are equal: a=b, then ac=bc.

Back 23

multiplication, multiplied

Front 24

If equals are __________ by nonzero equals, their quotients are equal: a=b, then a/c=b/c as long as c does not equal zero. What property does this represent?

Back 24

divided, division

Front 25

The _____________ property states that if a=b then either a or b may be _____________ for the other in an y equation.

Back 25

substitution , substituted

Front 26

If a=b and b=c, then a=c. What property does this represent?

Back 26

transitive property

Front 27

a=a, any quantity is equal to itself. This property is called the ____________ property.

Back 27

reflexive

Front 28

If a=b, then b=a, the positions of the expressions on either side of an equals sign may be reversed. What property is this?

Back 28

symmetric property

Front 29

If angles with measures add to 90 degrees, what are they called?

Back 29

complementary angles

Front 30

If two angles are complementary to the same angle or congruent angles, then they are congruent(=). Is this theorem true or false?

Back 30

true