Postulates, Theorems, And Converses

Front 1

Parallel Postulate

Back 1

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Front 2

Perpendicular Postulate

Back 2

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Front 3

Linear Pair Perpendicular Theorem

Back 3

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

Front 4

Perpendicular Transversal Theorem

Back 4

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Front 5

Lines Perpendicular to a Parallel Transversal theorem

Back 5

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Front 6

Transitive Property of Parallel lines

Back 6

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

Front 7

Corresponding Angles Theorem

Back 7

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Front 8

Alternate Exterior Angles Theorem

Back 8

If the two lines are parallel, then the theorem tells you that thealternate exterior angles are congruent to each other.

Front 9

Corresponding Angles Converse

Back 9

If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.

Front 10

Alternate Exterior Angles Converse

Back 10

If two lines are cut by a transversal so that the alternate exterior angles are congruent, then lines are parallel.

Front 11

Alternate Interior Angles Theorem

Back 11

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Front 12

Alternate Interior Angles Converse

Back 12

If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel.

Front 13

Consecutive Interior Angles Converse

Back 13

If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel.

Front 14

Segment Addition Postulate

Back 14

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

Front 15

Angle Addition Postulate

Back 15

If a ray lies in the interior of an angle, then the sum of the measures of the two smaller angles is equal to the larger angle.

Front 16

Two-point Postulate

Back 16

Through any two points there is exactly one line.

Front 17

Line-point Postulate

Back 17

A line contains at least two points.

Front 18

Three-point Postulate

Back 18

Through any three non co-linear points there exists exactly one plane.

Front 19

Plane-point Postulate

Back 19

A plane contains at least three non co-linear

Front 20

Line-Intersect Postulate

Back 20

If two lines intersect, then their intersection is exactly one point.

Front 21

Plane- line Postulate

Back 21

If two points lie in a plane, then the line containing them lies in the plane.

Front 22

Plane-Intersect Postulate

Back 22

If two planes intersect, then their intersection is exactly one line.

Front 23

Definition of a midpoint

Back 23

A midpoint separates a segment into two congruent segments.

Front 24

Definition of an Angle Bisector

Back 24

An angle bisector divides an angle into two congruent angles.

Front 25

Addition Property of Equality

Back 25

If you add the same number to both sides of an equation, then the equation remains true.

Front 26

Subtraction Property of

Back 26

If you subtract the same number from both sides of an equation, then the equation remains true.

Front 27

Multiplication/Division Property of Equality

Back 27

If you multiply of divide the same number on each side of an equation, then the equation remains true.

Front 28

Substitution Property of Equality

Back 28

If x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.

Front 29

Transitive Property of Equality or Congruence

Back 29

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

Front 30

Definition of a right angle

Back 30

A right angle equals 90 degrees.

Front 31

Definition of Congruence

Back 31

Congruent geometric segments have equal measures.

Front 32

Definition of Perpendicular

Back 32

Perpendicular lines intersect to create two right angles.

Front 33

Definition of Complementary Angles

Back 33

If the sum of two angles is equal to 90 degrees, then they are complementary.

Front 34

Definition of Supplementary Angles

Back 34

If the sum of two angles are 180 degrees, then the angles are supplementary.

Front 35

Linear Pair Postulate

Back 35

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

Front 36

Right Angles are Congruent

Back 36

If two angles are right angles, then they are congruent.

Front 37

Vertical Angles are Congruent

Back 37

If two angles are vertical angles, then they are congruent.

Front 38

Supplements of Congruent Angles

Back 38

If <1 & <2 are supp, and <4 & <2 are supp, then <1 & <4 are congruent.

Front 39

Complements of Congruent Angles

Back 39

If <1 & <2 are comp, and <4 & <2 are comp, then <1 &<4 are congruent.

Front 40

Corresponding Angles Theorem

Back 40

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Front 41

Alternate Interior Angles Theorem

Back 41

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Front 42

Alternate Exterior Angles Theorem

Back 42

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Front 43

Consecutive Interior Angles Theorem

Back 43

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Front 44

Corresponding Angle Converse Postulate

Back 44

If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

Front 45

Alternate Interior Angles Converse Theorem

Back 45

If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

Front 46

Alternate Exterior Angles Converse Theorem

Back 46

If two lines are cut by a transversal to that a pair of alternate exterior angles are congruent, then the lines are parallel.

Front 47

Consecutive Interior Angles Converse Theorem

Back 47

If two lines are cut by a transversal so that a pair of consecutive interior angles are congruent, then the lines are parallel.

Front 48

Base Angles Theorem

Back 48

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

Front 49

Converse of the Base Angles Theorem

Back 49

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

Front 50

Corollary to 5.2

Back 50

If a triangle is equilateral, then it is also equiangular.

Front 51

Corollary to 5.3

Back 51

If a triangle is equiangular, then it is also equilateral.

Front 52

Side-Angles-Side Congruence Theorem

Back 52

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

Front 53

Side-Side-Side Congruence Theorem

Back 53

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Front 54

Hypotenuse-Leg Congruence Theorem

Back 54

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are congruent.