Definitions, Theorems, Postulates

Front 1

Colinear points

Back 1

Points that lie on the same line

Front 2

Coplaner points

Back 2

Points that are on the same plane

Front 3

Parallel lines

Back 3

Lines in the same plane that don't intersect

Front 4

Segment addition postulate

Back 4

Little pieces add up to big piece

Front 5

Midpoint

Back 5

The point that divides the segment into two congruent pieces

Front 6

Angle bisector

Back 6

A ray that divides an angle into two angles

Front 7

Angle addition postulate

Back 7

Two angles = one big angle

Front 8

Transformation

Back 8

An object that moves or changes to form a new object

Front 9

Image

Back 9

Object after transformation

Front 10

Preimage

Back 10

Object before transformation

Front 11

Translation

Back 11

The figure slides to a new location

Front 12

Reflections

Back 12

Creates a mirror image of the original across a line of reflection

Front 13

Rotation

Back 13

Turns a figure about a fixed point

Front 14

Dilation

Back 14

Stretch or shrink

Front 15

Rigid motion

Back 15

Transformation that changes the position of figure without changing the size/shape

Front 16

Conjecture

Back 16

Statement that is believed to be true

Front 17

Inductive reasoning

Back 17

Process of reasoning that a rule is true because if specific cases.

Front 18

Deductive reasoning

Back 18

Process of using logic to draw conclusions

Front 19

Counter example

Back 19

Example that proves conjecture false

Front 20

Conditional statement

Back 20

"If" "Then" statement

Front 21

Transitive property

Back 21

When two things are equal to the same thing, then they are equal to each other

Front 22

Complementary angles

Back 22

Angles that add up to 90 degrees

Front 23

Supplementary angles

Back 23

Angles that add up to 180 degrees

Front 24

Adjacent angles

Back 24

Two angles that share a common vertex and side

Front 25

Linear pair

Back 25

Pair of adjacent angles whose non-common sides are opposite rays

Front 26

Opposite rays

Back 26

Rays that share a common end point and form a line

Front 27

Linear Pair Theorem

Back 27

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

Front 28

Perpendicular lines

Back 28

Lines that intersect at right angles

Front 29

Perpendicular bisector

Back 29

A line perpendicular to the segment at the segment's midpoint

Front 30

Angle of rotation

Back 30

Tells the degree through which points rotate around the center of rotation

Front 31

Symmetry

Back 31

Rigid motion that maps the figure onto its self

Front 32

Line symmetry

Back 32

Reflection maps figure onto its self

Front 33

Lines of symmetry

Back 33

Lines that map figure onto its self

Front 34

Rotational symmetry

Back 34

Rotation that maps figure onto its self

Front 35

CPCTC

Back 35

If two figures are congruent, then corresponding sides are congruent and corresponding angles are congruent

Front 36

Definition of congruence

Back 36

Congruent sides are same length; congruent angles are same degree

Front 37

Vertical angles

Back 37

Two angles in which their sides form two pairs of opposite rays

Front 38

Skew lines

Back 38

Two lines that do not intersect and are not coplanar

Front 39

Parallel planes

Back 39

Two planes that do not intersect

Front 40

Transversal

Back 40

A line that intersects two or more coplanar lines at different points

Front 41

Corresponding angles

Back 41

Two angles that have corresponding positions

Front 42

Alternate Interior angles

Back 42

Two angles that lie between the two lines and in opposite sides of the transversal

Front 43

Alternate Exterior Angles

Back 43

Two angles that lie outside the two lines and on opposite sides of the transversal

Front 44

Consecutive Interior Angles

Back 44

Two angles that lie between the two lines and on the same side of the transversal

Front 45

Vertical angles Congruence Theorem

Back 45

Vertical angles are congruent

Front 46

Alt. Ex. Angles Converse Thm

Back 46

If the alt ex angles are congruent then the lines are parallel

Front 47

Corres. Angles Converse Thm

Back 47

If the corres angles are congruent then the lines are parallel

Front 48

Consec. Int. Angles Converse Thm

Back 48

If the consec int angles are supp. then the lines are parallel

Front 49

Alt. Int. Angles Converse Thm

Back 49

If the alt int angles are congruent then the lines are parallel

Front 50

Transitive Property of Parallel Lines

Back 50

If two lines are parallel to the same line, then they are parallel to each other

Front 51

Parallel Postulate

Back 51

For any line l, you can always construct a parallel line thru a point that is not on l

Front 52

Perpendicular Bisector Theorem

Back 52

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

Front 53

Converse of the Perpendicular Bisector Theorem

Back 53

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

Front 54

ASA

Back 54

Two angles and the included side are congruent

Front 55

SSS

Back 55

All three sides are congruent

Front 56

AAS

Back 56

Two angles and a non included side are congruent

Front 57

SAS

Back 57

Two sides and the included angle are congruent

Front 58

CPCTC

Back 58

Once you prove the triangles are congruent then you know all the sides and angles are congruent too.

Front 59

HL

Back 59

The hypotenuse and one of the legs are congruent

Front 60

Third Angles Theorem

Back 60

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent

Front 61

Right Angles Congruence Theorem

Back 61

All right angles are congruent

Front 62

Congruent Supplements Theorem

Back 62

If angle 1 and angle 2 are supplementary and angle 3 and angle 2 are supplementary, then angle 1 is congruent to angle 3

Front 63

Congruent Complements Theorem

Back 63

If angle 4 and angle 5 are complementary and angle 6 and angle 5 are complementary, then angle 4 is congruent to angle 6

Front 64

Reflexive Property of Equality

Back 64

a=a

Front 65

Symmetric Property of Equality

Back 65

If a=b then b=a

Front 66

Transitive Property of Equality

Back 66

If a=b and b=c, then a=c

Front 67

Substitution Property

Back 67

If a=b, then b and be substituted for a in any expression