Geometry Postulates, Theorems

Front 1

Through any two different points there is exactly one _____.

Back 1

line.

Front 2

Through any three points that are not on one line, there is exactly one _____.

Back 2

plane.

Front 3

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

Back 3

plane.

Front 4

If two different planes intersect, then their intersection is a _____.

Back 4

line.

Front 5

Between any two points there is a unique _____.

Back 5

distance.

Front 6

A line contains at least _____.

Back 6

two points.

Front 7

A plane contains at least _____.

Back 7

three points not all on one line.

Front 8

Space contains at least _____.

Back 8

four points not all on one plane.

Front 9

If two parallel lines are cut by a transversal, corresponding angle are _____.

Back 9

congruent.

Front 10

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

Back 10

parallel.

Front 11

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

Back 11

congruent. (SSS postulate)

Front 12

SSS postulate

Back 12

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

Front 13

If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, the triangles are _____.

Back 13

congruent. (SAS postulate)

Front 14

SAS postulate

Back 14

If 2 sides and the included angle of one triangle are congruent to 2 sides + the included angle of another triangle, the triangles are congruent.

Front 15

HL postulate

Back 15

If the hypotenuse and a leg of one rt triangle are congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.

Front 16

≅ means?

Back 16

congruent

Front 17

If the hypotenuse and a leg of one rt triangle are congruent to the hypotenuse and a leg of another right triangle, the triangles are _____.

Back 17

congruent. (HL postulate)

Front 18

Angle measurement postulate

Back 18

To every angle there corresponds a unique real number greater than 0 and less than 180.

Front 19

ASA postulate (angle - side - angle)

Back 19

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, the triangles are congruent.

Front 20

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, the triangles are _____.

Back 20

congruent. (ASA postulate)

Front 21

If 2 angles of one triangle are congruent to 2 angles of another triangle, the triangles are _____.

Back 21

similar. (AA postulate)

Front 22

AA postulate (angle - angle)

Back 22

If 2 angles of one triangle are congruent to 2 angles of another triangle, the triangles are similar.

Front 23

Arc Addition postulate

Back 23

If the intersection of arcs DE and EF of a circle is the single point E, the mDE + mEF = mDEF.

Front 24

If the intersection of arcs DE and EF of a circle is the single point E, the mDE + mEF = _____.

Back 24

mDEF. (Arc Addition postulate)

Front 25

Corresponding to each polygonal region there is a unique positive number called the _____.

Back 25

area of that region.

Front 26

If two triangles are congruent, then the regions they bound have _____.

Back 26

the same area.

Front 27

If a polygonal region is the union of n non-overlapping polygonal regions, then its area is _____.

Back 27

the sum of the areas of those n regions.

Front 28

The area of a rectangle is the product of _____.

Back 28

the length of a base and the length of an altitude to that base. (A=bh)

Front 29

If two polygons are similar, they can be separated into the same number of _____ similar each to each and in _____.

Back 29

triangles similar each to each and in corresponding positions.

Front 30

THEOREM: If two lines intersect, they intersect in _____.

Back 30

exactly one point.

Front 31

THEOREM: If a point lies outside a line, exactly one plane _____.

Back 31

contains the line and the point.

Front 32

THEOREM: If two lines intersect, exactly _____.

Back 32

one plane contains both lines.

Front 33

THEOREM: On a ray there is exactly ____ at a given distance from _____.

Back 33

one point at a given distance from the endpoint of the ray.

Front 34

THEOREM: A segment has exactly one _____.

Back 34

midpoint.

Front 35

Angle Addition theorem

Back 35

If the ray OE lies between ray OD and ray OF in a half-plane, the m angle DOE + m angle EOF = m angle DOF

Front 36

THEOREM: If the ray OE lies between ray OD and ray OF in a half-plane, the m angle DOE + m angle EOF = _____.

Back 36

m angle DOF (Angle Addition theorem)

Front 37

def. of Theorem

Back 37

A statement that can be proved.

Front 38

def. of Postulate or Axiom

Back 38

Fundamental statements accepted as true without proof.

Front 39

THEOREM: If the exterior sides of two adjacent angles are opposite rays, the angles are _____.

Back 39

supplementary

Front 40

THEOREM: An angle has exactly one _____.

Back 40

bisector.

Front 41

THEOREM: All rt angles are _____.

Back 41

congruent.

Front 42

THEOREM: If two lines are perpendicular, the meet to form _____.

Back 42

right angles.

Front 43

THEOREM: If two lines meet for form a right angle, the lines are _____.

Back 43

perpendicular.

Front 44

THEOREM: If two adjacent acute angles have their exterior sides in perpendicular lines, the angles are _____.

Back 44

complementary.

Front 45

THEOREM: In a plane, through a given point of a line, there is exactly one line _____.

Back 45

perpendicular to the line.

Front 46

THEOREM: If two angles are supplementary to the same angle or to congruent angles, they are _____.

Back 46

congruent to each other.

Front 47

THEOREM: If two angles are complementary to the same angle or to congruent angles, they are _____.

Back 47

congruent to each other.

Front 48

THEOREM: If two lines intersect, the vertical angles formed are _____.

Back 48

congruent.

Front 49

THEOREM: Congruence of segments is _____. (3 qualities)

Back 49

reflexive,symmetric and transitive.

Front 50

THEOREM: Congruence of angles is _____. (3 qualities)

Back 50

reflexive,symmetric and transitive.

Front 51

THEOREM: If two parallel planes are cut by a third plane, the lines of intersection are _____.

Back 51

parallel.

Front 52

THEOREM: If a transversal is perpendicular to one of two parallel lines, it is _____ to _____ also.

Back 52

it is perpendicular to the other one also.

Front 53

THEOREM: If two parallel lines are cut by a tranversal, alternate interior lines are _____.

Back 53

congruent.

Front 54

THEOREM: If two parallel lines are cut by a transversal, _____ are congruent.

Back 54

alternate interior lines

Front 55

THEOREM: Through a point outside a line not more than one ____ can be drawn to the line.

Back 55

parallel (or perpendicular)

Front 56

THEOREM: Through a point outside a line a _____ can be drawn to the line.

Back 56

parallel

Front 57

THEOREM: Through a point outside a line exactly one line can be drawn _____.

Back 57

perpendicular (or parallel) to the line.

Front 58

THEOREM: In a plane, if two lines are perpendicular to a third one, they are _____.

Back 58

parallel to each other.

Front 59

THEOREM: If two lines are cut by a transversal so that alternate interior angles are congruent, the lines are _____.

Back 59

parallel.

Front 60

THEOREM: The sum of the measures of the angles of a triangle is _____.

Back 60

180.

Front 61

THEOREM: The measure of an exterior angle of a triangle is equal to the sum of the measures of _____.

Back 61

the two remote interior angles

Front 62

THEOREM: The sum of the measures of the angle of a convex quadrilateral is _____.

Back 62

360.

Front 63

THEOREM: Congruence of triangles is _____. (3 qualities)

Back 63

reflexive, symmetric and transitive.

Front 64

THEOREM: If the legs of one right triangle are congruent to the legs of another right triangle, the triangles are _____.

Back 64

congruent. (LL theorem)

Front 65

LL Theorem. (leg - leg)

Back 65

If the legs of one right triangle are congruent to the legs of another right triangle, the triangles are congruent.

Front 66

THEOREM: If two angles and a not-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are _____.

Back 66

congruent. (AAS theorem)

Front 67

AAS theorem. (angle - angle - side)

Back 67

If two angles and a not-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Front 68

THEOREM: If two sides of a triangle are congruent, then the _____ opposite those sides are _____.

Back 68

angles opposite those sides are congruent. (Base angles of an isosceles triangle are congruent)

Front 69

THEOREM: If two angles of a triangle are congruent, then the _____ opposite those angles are _____.

Back 69

sides opposite those angles are congruent.

Front 70

THEOREM: A diagonal of a parallelogram separates the parallelogram into _____.

Back 70

two congruent triangles.

Front 71

THEOREM: The diagonals of a parallelogram _____ each other.

Back 71

bisect

Front 72

THEOREM: If two sides of a quadrilateral are _____ and _____, the quadrilateral is a parallelogram.

Back 72

congruent and parallel

Front 73

THEOREM: If both pairs of _____ sides of a quadrilateral are _____, the quadrilateral is a parallelogram.

Back 73

opposite sides ... congruent

Front 74

THEOREM: If the _____ of a quadrilateral bisect each other, the quadrilateral is a parallelogram.

Back 74

diagonals

Front 75

THEOREM: The segment joining the midpoints of two sides of a triangle is parallel to _____ and its length is _____.

Back 75

the third side and its length is half the length of the third side.

Front 76

THEOREM: If three parallel lines cut of congruent segments on one transversal, they cut off _____ segments on every _____.

Back 76

congruent segments of every transversal.

Front 77

THEOREM: The diagonals of a rectangle are _____.

Back 77

congruent.

Front 78

THEOREM: The diagonals of a rhombus are _____.

Back 78

perpendicular

Front 79

THEOREM: Each diagonal of a rhombus _____ two angles of the rhombus.

Back 79

bisects

Front 80

THEOREM: The median of a trapezoid is _____ to the bases; it has a length equal to _____ of the bases

Back 80

parallel; half the sum

Front 81

THEOREM: Base angles of an _____ trapezoid are _____.

Back 81

isosceles trapezoid are congruent.

Front 82

THEOREM: The diagonals of an isosceles trapezoid are _____.

Back 82

congruent.

Front 83

The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Back 83

Pythagorean Theorem

Front 84

def. Complementary Angles

Back 84

two angles the sum of whose measure is 90. Each angle is called a complement of the other.

Front 85

def. Supplementary Angles

Back 85

two angles the sum of whose measure is 180. Each angle is called a supplement of the other.

Front 86

def. Induction

Back 86

The process of finding a general principle based upon the evidence of specific cases.

Front 87

def. Deduction

Back 87

The process of accepting some statements as true and reasoning from them to a conclusion.

Front 88

Law of Detachment

Back 88

Whenever p→q is true and p is true, the q is true