Geometry H Ch1-4 & 5-9 Theorems And Postulates

Front 1

Distance Postulate

Back 1

To every pair of different points there corresponds a unique positive number

Front 2

Ruler Postulate*

Back 2

The points of a line can be placed in correspondence with the real numbers in such a way that

1. to every point of the line there corresponds exactly one real number

2. to every real number there corresponds exactly one point of the line and

3. the distance between any two points is the absolute value of the difference of the corresponding numbers.

Front 3

The Ruler Placement Postulate*

Back 3

Given two points P and Q of a line, the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is positive.

Front 4

Theorem 2-3 (coordinate betweeness)

Back 4

Let A, B, and C be points of a line, with coordinates, x,y, and z respectively. If x < y < z, then A-B-C.

Front 5

Theorem 2-4 (betweeness)

Back 5

If A, B, and C are three different point of the same line, then exactly one of them is between the other two.

Front 6

The Point-Plotting Theorem (Theorem 2-5)

Back 6

Let Ray AB be a ray, and let x be a positive number. Then there is exactly one point P of Ray AB such that AP=x.

Front 7

The Midpoint Theorem (Theorem 2-6)

Back 7

Every segment has exactly one midpoint

Front 8

The Line Postulate

Back 8

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

Front 9

Theorem 3-1 (Line intersection)

Back 9

If two different lines intersect, their intersection contains only one point.

Front 10

The Plane-Space Postulate

Back 10

a) Every plane contains at least 3 different noncollinear points.

b) Space contains at least 4 different noncoplanar points

Front 11

The Flat Plane Postulate

Back 11

If two points of a line lie in a plane, then the line lies in the same plane

Front 12

Theorem 3-2 (Line and Plane intersection)

Back 12

If a line intersects a plane not containing it, then the intersection contains only one point.

Front 13

The Plane Postulate

Back 13

Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane.

Front 14

Theorem 3-3 (Line, point, plane)

Back 14

Given a line and a point not on the line, there is exactly one plane containing both

Front 15

Theorem 3-4 (Intersecting lines & plane)

Back 15

Given two intersecting lines, there is exactly one plane containing both.

Front 16

Intersection of Planes Postulate

Back 16

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

Front 17

Definition of Convex

Back 17

A set M is called convex if for every two points P and Q of the set the entire segment of segment PQ lies in M.

Front 18

The Plane Separation Postulate*

Back 18

Given a line and a plane containing it. The points of the plane that do not lie on the line form two sets such that

1) each of the sets is convex, and

2) if P is in one of the sets and Q is in the other, then the segment of segment PQ intersects the line.

Front 19

Definition of Half-planes ,sides, edges, and opposite sides

Back 19

Given a line L and a plane E containing it, the two sets described in the Plane Separation Postulate are called half-planes or sides of L, and L is called the edge of each of them. If P lies in one of the half-planes and Q lies in the other, then we say that P and Q lie on opposite sides of L.

Front 20

The Space Separation Postulate*

Back 20

The points of space that doe not lie in a given plane form two sets, such that

1) each of the sets is convex, and

2) If P is in one of the sets and Q is in the other, then the segment, segment PQ intersects the plane.

Front 21

Definition of Half-Space

Back 21

The two sets described in the Space Separation Postulate are called half-spaces, and the given plane is called the face of each of them.

Front 22

Definition of Ray, angle, and vertex

Back 22

If two rays have the same end point, but do not lie on the same line, then their union is an angle. The two rays are called its sides, and their common end point is called its vertex. If the rays are ray AB and ray AC, then the angle is noted by

Front 23

Definition of Interior and Exterior of angles

Back 23

The interior of < BAC is the set of all points P in the plane of

1) P and B are on the same side of line AC, and

2) P and C are on the same side of line AC.

The exterior of < BAC is the set of all points of the plane of < BAC that lie neither on the angle nor in its interior.

Front 24

Definition of Interior and Exterior of a triangle

Back 24

A point lies in the interior of a triangle if it lies in the interior of each of the angles of the triangle. A point lies in the exterior of a triangle if it lies in the plane of the triangle but does not lie on the triangle or in the interior.

Front 25

The Angle Measurement Postulate

Back 25

To every angle < BAC there corresponds a real number between 0 and 180.

Front 26

Definition of the measure of an angle

Back 26

The number given by the Angle Measurement Postulate is called the measure of

Front 27

The Angle Construction Postulate

Back 27

Let ray AB be a ray on the edge of the half-plane H. For every number r between 0 and 180 there is exactly one ray, ray AP, with P in H , such that m

Front 28

The Angle Addition Postulate*

Back 28

If D is in the interior of

m

Front 29

Definition of Linear Pair

Back 29

If ray AB and ray AD are opposite rays, and ray AC is any other ray, then

Front 30

Definition of Supplement and Supplementary

Back 30

If the sum of the measures of two angles is 180, then the angles are called supplementary, and each is called a supplement of the other.

Front 31

The Supplement Postulate

Back 31

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

Front 32

Definition of types of angles

Back 32

A right angle is an angle having measure 90. An angle with measure less than 90 is called acute. An angle with measure greater than 90 is called obtuse.

Front 33

Definition of Complementary angles

Back 33

If the sum of the measures of two angles is 90, then they are called complementary, and each of them is called a complement of the other.

Front 34

Definition of Congruent Angles

Back 34

Two angles with the same measure are called congruent.

Front 35

Definition of Perpendicular rays & lines

Back 35

Two rays are perpendicular if they are the sides of a right angle. Two lines are perpendicular if they contain a pair of perpendicular rays.

Front 36

Definition of Perpendicular sets

Back 36

Two sets are perpendicular if (1) each of them is a line, a ray, or a segment, (2) they intersect, and (3) the lines containing them are perpendicular.

Front 37

Theorem 4-1 (congruence between angles)

Back 37

Congruence between angles is an equivalence relation

Front 38

Theorem 4-2 (congruent angles in a linear pair)

Back 38

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

Front 39

Theorem 4-3 (complementary angles)

Back 39

If two angles are complementary, then both are acute.

Front 40

Theorem 4-4 (right angle congruence)

Back 40

Any two right angles are congruent.

Front 41

Theorem 4-5 (right angle)

Back 41

If two angles are both congruent and supplementary, then each is a right angle.

Front 42

The Supplement Theorem

Back 42

Supplements of congruent angles are congruent.

Front 43

The Complement Theorem

Back 43

Complements of congruent angles are congruent

Front 44

Definition of vertical angles

Back 44

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

Front 45

The Vertical Angle Theorem

Back 45

Vertical angles are congruent

Front 46

Theorem 4-9 (perpendicular lines & rt. angles)

Back 46

If two lines are perpendicular, they form four right angles

Front 47

Definition of union & intersection

Back 47

The union of two sets is the set of all elements that belong to one or both sets. The intersection of two or more sets is the set of all elements common to the sets.

Front 48

Definition of intersect

Back 48

Two sets intersect if there are one or more elements that are common to the sets.

Front 49

Commutative Property of Addition

Back 49

a + b = b + a

Front 50

Commutative Property of Multiplication

Back 50

ab = ba

Front 51

Associative Property of Addition

Back 51

(a + b) + c = a + (b + c)

Front 52

Associative Property of Multiplication

Back 52

(ab)c = a(bc)

Front 53

Distributive Property

Back 53

a(b + c) = ab + ac

Front 54

Addition Property of Equality

Back 54

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

Front 55

Subtraction Property of Equality

Back 55

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

Front 56

Division Property of Equality

Back 56

If a = b and c != 0, then a/c = b/c

Front 57

Multiplication Property of Equality

Back 57

if a =b and c = d, then ac = bd

Front 58

Transitive Property of Equality

Back 58

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

Front 59

Trichotomy Property

Back 59

For every x and y, on and only one of the following conditions hold: x < y, x = y, x > y

Front 60

Transitive Property of Inequalities

Back 60

If x < y and y < z, then x < z.

Front 61

Addition Property of Inequalities

Back 61

If a < b and x<= y, then a + x < b + y

Front 62

Multiplication Property of Inequalities

Back 62

If x < y and a > 0, then ax < ay

Front 63

Theorem 2-1

Back 63

If a - b > 0, then a > 0

Front 64

Theorem 2- 2

Back 64

If a = b + c and c > 0 then a > b

Front 65

Existence of Square Roots

Back 65

Every positive number has exactly one positive square root

Front 66

Definition of Absolute Value

Back 66

The absolute value of a number x is denoted by

|x| with the following rules:

1) if x >= 0, then |x| = x.

2) if x < 0 then |x| is the corresponding positive number

Front 67

The angle measurement postulate

Back 67

To every angle BAC there corresponds a real number between 0 and 180

Front 68

Angle addition postulate

Back 68

If D is in the interior of angle BAC then the measure of angle BAC = the measure of angle BAD + the measure of angle DAC

Front 69

The supplement postulate

Back 69

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

Front 70

Definition of triangle congruence

Back 70

Two triangles are congruent if all three sides and the measure of all three angles are the same on both triangles

Front 71

Definition of congruence in segments

Back 71

Two segments are congruent if they have the same length

Front 72

Definition of what is included in a triangle

Back 72

A side of a triangle is said to be included by the angles whose vertices are the end points of the segment.

An angle of a triangle is said to be included by the sides of the triangle which lie in the sides of the angle.

Front 73

Congruence of segments (Theorem 5-1)

Back 73

Congruence of segments is an equivalence relation

Front 74

Congruence of triangles (Theorem 5-2)

Back 74

Congruence of triangles is an equivalence relation

Front 75

SAS triangle congruence postulate

Back 75

If you have two triangles that have two congruent sides and the included angle is also congruent, then both triangles are congruent.

Front 76

ASA triangle congruence postulate

Back 76

If you have two triangles that have two congruent angles and the included side is also congruent, then both triangles are congruent.

Front 77

SSS triangle congruence postulate

Back 77

If you have two triangles that have three congruent sides then both triangles are congruent.

Front 78

Definition of a Bisector

Back 78

If D is in the interior of

Front 79

Theorem 5- 3 The Angle Bisector Theorem

Back 79

Every angle has one and only one bisector.

Front 80

Theorem 5-4 The Isosceles Triangle Theorem

Back 80

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

Front 81

Corollary 5-4.1

Back 81

Every equilaterl triangle is equiangular

Front 82

Theorem 5-5

Back 82

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

Front 83

Corollary 5-5.1

Back 83

Every equiangular triangle is equilateral

Front 84

Theorem 5-4

Back 84

Given Triangle ABC. If AB=AC the

Front 85

Theorem 5-5

Back 85

Given Triangle ABC. If

Front 86

Theorem

Back 86

A triangle is equiangular if and only if it is equilateral

Front 87

Definition of a Quadrilateral

Back 87

Let A, B, C, and D be four coplanar points. If no three of these points are collinear, and the segments AB, BC, CD, and DA intersect only at their end points, then the union of the four segments is called a guadrilateral. The four segments are called its sides and the points A, B, C, and D are called its vertices. The angles

Front 88

Def. of a rectangle

Back 88

If all four angles of the quadrilateral are right angles, then the quadrilateral is a rectangle

Front 89

Def. of a median

Back 89

A median of a triangle is a segment whose end points are a verex of the triangle and the midpoint of the opposite side

Front 90

Def. of a square

Back 90

If all four of the angles and all four sides are congruent then the quadrilateral is a square.

Front 91

Definition of an angle bisector of a triangle

Back 91

A segment is an angle bisector of a triangle if (1) it lies in the ray which bisects an angle of the triangle, and (2) its end points are the vertex of this angle and a point of the opposite side.

Front 92

Theorem 6-1

Back 92

In a given plane, through a given point of a given line, there is one and only one line perpendicular to the given line.

Front 93

Theorem 6-2: The Perpendicular Bisector Theorem

Back 93

The perpendicular bisector of a segment, in a plane, is the set of all points of the plane that are equidistant from the end points of the segment.

Front 94

Definition of a perpendicular bisector

Back 94

In a given plane, the perpendicular bisector of a segment is the line which is perpendicular to the segment at its midpoint

Front 95

Corollary 6-2.1

Back 95

Given a segment AB and a line L in the same plane. If two points of L are each equidistant from A and B, then L is the perpendicular bisector of line segment AB.

Front 96

Theorem 6-3

Back 96

Through a given external point there is at least one line perpendicular to a given line.

Front 97

Theorem 6-4

Back 97

Through a given external point there is at most one line perpendicular to a given line.

Front 98

Corollary 6-4.1

Back 98

No triangle has two right angles

Front 99

Def. of a right triangle

Back 99

A right triangle is a triangle one of whoe angles is a right angle. The side opposite the right angle is called the hypotenuse and the other two sides are called the legs

Front 100

Theorem 6-5

Back 100

If M is between A and C on a line L, then M and A are on the same side of any other line that contains C.

Front 101

Theorem 6-6

Back 101

If M is between B and C, and A is any point not on line BC, then M is in the interior of

Front 102

Definition of inequalities between segments

Back 102

Line Segment AB < Line Segment CD if AC

Front 103

Definition of inequalities between angles

Front 104

Definition of remote interior angles

Front 105

Theorem 7-2. The Exterior Angle Theorem

Back 105

An exterior angle of a triangle is greater than each of its remote interior angles

Front 106

Corollary 7-2.1

Back 106

If a triangle has one right angle, then its other angles are acute

Front 107

SAA correspondence

Back 107

Given a correspondence ABC <-> DEF between two triangles. If a pair of corresponding sides are congruent, and two pairs of corresponding angles are congruent, then the correspondence is called an SAA correspondence. Side Angle Angle.

Front 108

Theorem 7-3. The SAA Theorem

Back 108

Every SAA correspondence is a congruence

Front 109

Theorem 7-4. The Hypotenuse-Leg Theorem

Back 109

Given a correspondence between two right triangles. If the hypotenuse and one leg of one of the triangles are congruent to the corresponding parts of the second triangle, then the correspondence is a congruence.

Front 110

Theorem 7-5.

Back 110

If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side

Front 111

Theorem 7-6

Back 111

If two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the longer side is opposite the larger angle.

Front 112

Theorem 7-7. The first Minimum Theorem

Back 112

The shortest segment joining a point to a line is the perpendicular segment.

Front 113

Theorem 7-8 The Triangle Inequality

Back 113

The sum of the lengeth of any two sides of a triangle is greater than tthe length of the third side

Front 114

Theorem 7-9 The Hinge Theorem

Back 114

If two sides of one triangle are congruent, respectively, to two sides of a second triangle, and the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second.

Front 115

Theorem 7-10 The Converse Hinge Theorem

Back 115

If two sides of one triangle are congruent respectively to two sides of a second triangle, and the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.

Front 116

Definition of Altitude

Back 116

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

Front 117

Definition of Perpendicularity for lines and planes

Back 117

A line and a plane are perpendicular if they intersect and if every line lying in the plane and passing through the point of intersection is perpendicular to the given line. If the line L and the plane E are perpendicular, then we write L perpendicular E or E perpendicular to L. If P is their point of intersection, then we say that L is perpendicular to E at P.

Front 118

Theorem 8-1

Back 118

If B and C are equidistant from P and Q, then every point between B and C is equidistant from P and Q.

Front 119

Theorem 8-2. The Basic Theorem on Perpendiculars

Back 119

If a line is perpendicular to each of two intersecting lines at their point of intersection, then it is perpendicular to the plane that contains them.

Front 120

Theorem 8-3

Back 120

Through a given point of a given line there passes a plane perpendicular to the given line.

Front 121

Theorem 8-4

Back 121

If a line and a plane are perpendicular, then the plane contains every line perpendicular to the given line at its point of intersection with the given plane.

Front 122

Theorem 8-5

Back 122

Through a given point of a given line there is only one plane perpendicular to the line.

Front 123

Theorem 8-6. The Perpendicular Bisecting Plane Theorem

Back 123

The perpendicular bisecting plane of a segment is hte set of all points equidistant from the end points of the segment.

Front 124

Theorem 8-7

Back 124

Two lines perpendicular to the same plane are coplanar

Front 125

Theorem 8-8

Back 125

Through a given point there passes one and only one plane perpendicular to a given line

Front 126

Theorem 8-9

Back 126

Through a given point there passes one and only one line perpendicular to a given plane.

Front 127

Theorem 8-10 The Second Minimum Theorem

Back 127

The shortest segment to a plane from an external point is the perpendicular segment

Front 128

Definition of distance to a plane

Back 128

The distance to a plane from an external point is the length of the perpendicular segment from the point to the plane.

Front 129

Definition of skew lines and parallel lines

Back 129

Two lines are skew lines if they do not lie in the same plane. Two lines are parallel if (1) they are coplanar and (2) they do not intersect.

Front 130

Theorem 9-1

Back 130

Two parallel lines lie in exactly one plane

Front 131

Theorem 9-2

Back 131

In a plane, if two lines are both perpendicula to the same line, then they are parallel

Front 132

Theorem 9-3 Existence of Parallels

Back 132

Let L be a line and let P be a point not on L. Then there is at least one line through P, parallel to L.

Front 133

Definition of Transversal

Back 133

A transversal of two coplanar lines is a line which intersects them in two different planes

Front 134

Definition of Alternate interior angles

Back 134

Given two lines L1 and L2, cut by a transversal T at points P and Q. Let A be a point of L1 and let B be a point of L2, such that A and B lie on opposite sides of T. Then

Front 135

Theorem 9-4

Back 135

If two lines are cut by a transversal, and one pair of alternate interior angles are congruent, then the other pair of alternate interior angles are also congruent.

Front 136

Theorem 9-5 The AIP Theorem

Back 136

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

Front 137

Definition of Corresponding angles

Back 137

Given two lines cut by a transversal. If < x and

Front 138

Definition of interior angles on the same side of the transversal

Back 138

Given two lines cut by a transversal. If (1)

Front 139

Theorem 9-6

Back 139

Given two lines cut by a transversal. If a pair of corresponding angles are congruent, then a pair of alternate interior angles are congruent

Front 140

Theorem 9-7 The CAP Theorem

Back 140

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

Front 141

Theorem 9-8

Back 141

Given two lines cut by a transversal. If a pair of interior angles on the same side of the transversal are supplementary, the line are parallel.

Front 142

Postulate 18. The Parallel Postulate

Back 142

Through a given external point there is only one parallel to a given line.

Front 143

Theorem 9-9. The PAI Theorem

Back 143

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

Front 144

Corollary 9-9.1 The PCA Corollary

Back 144

If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent.

Front 145

Corollary 9-9.2

Back 145

If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.

Front 146

Theorem 9-10

Back 146

In a plane, if a line intersects on of the two parallel lines in only one point, then it intersects the other.

Front 147

Theorem 9-11

Back 147

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

Front 148

Theorem 9-12

Back 148

In a plane, if a line is perpendicular to one of two parallel lines it is perpendicular to the other

Front 149

Theorem 9-13

Back 149

For every triangle, the sum of the measures of the angles is 180.

Front 150

Corollary 9-13.1

Back 150

Given a correspondence between two triangles. If two pairs of corresponding angles are congruent, then the third pair of corresponding angles are also congruent.

Front 151

Corollary 9-13.2

Back 151

The acute angles of a right triangle are complementary.

Front 152

Corollarry 9-13.3

Back 152

For any triangle, the measure of an exterior angle is the sume of the measurres of the two remote interior angles.

Front 153

Definition of quadrilateral

Back 153

Let A,B, C and D be four points of the same plane. If no three of these points are colinear, and the segments of AB, BC, CD, and DA intersect only at their end points, then the union of these four segments is called a quadrilateral The four segments are called its sides, and the points A, B, C, and D are called its vertices. The angles

Front 154

Definition of Convex Quad.

Back 154

A quadrilateral is convex if no two of its vertices lie on the opposite sides of a line containing a side of the quadrilateral

Front 155

Definitions of Opposite sides, Consecutive sides, and Diagonal sides of a Quadrilateral

Back 155

Two sides of a quadrilateral are opposite if they do not intersect. Two of its angles are opposite if they do not have a side of the quadrilateral in common. Two sides are consecutive if they have a common end point. Two angles are consecutive if they have a side of the quadrilateral in common. A diagonal of a quadrilateral is a segment joining two nonconsecutive vertices.

Front 156

Definition of a parallelogram

Back 156

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel

Front 157

Definition of a trapezoid

Back 157

A trapezoid is a quadrilateral in which one and only one pair of opposite sides are parallel. The parallel sides are called the bases of the trapezoid. The segment joining the midpoints of the nonparallel sides is called the median

Front 158

Theorem 9-14

Back 158

Each diagonal separates a parallelogram into two congruent triangles.

Front 159

Theorem 9-15

Back 159

In a parallelogram, any two opposite sides are congruent.

Front 160

Corollary 9-15.1

Back 160

If two lines are parallel, then all points of each line are equidistant from the other line.

Front 161

Definition of distance between two prallel lines

Back 161

The distance between two parallel lines is the distance from any point of one to the other

Front 162

Theorem 9-16

Back 162

In a parallelogram, any two opposite angles are congruent

Front 163

Theorem 9-17

Back 163

In a parallelogram, any two consecutive angles are supplementary.

Front 164

Theorem 9-18

Back 164

The diagonal of a parallelogram bisect each other.

Front 165

Theorem 9-19

Back 165

Given a quadrialateral in which both pairs of opposite sides are congruent. Then t he quadrilateral is a parallelogram.

Front 166

Theorem 9-20

Back 166

If two sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram

Front 167

Theorem 9-21

Back 167

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Front 168

Theorem 9-22 The Midline Theorem

Back 168

The segment between the midpoints of two sides of a triangle is parallel to the third side and half as long

Front 169

Definition of Rhombus, Rectangle, and Square

Back 169

A rhombus is a parallelogram all of whose sides are congruent. A rectangle is a parallelogram all of whose angles are right angles. A square is a rectangle all of whose sides are congruent.

Front 170

Theorem 9-23

Back 170

If a parallelogram has one right angle, then it has four right angles and the parallelogram is a rectangle.

Front 171

Theorem 9-24

Back 171

In a rhombus, the diagonals are perpendicular to one another

Front 172

Theorem 9-25

Back 172

If the diagonals of a quadrilateral bisect each other and are perpendicular, then the quadrilateral is a rhombus.

Front 173

Theorem 9-26

Back 173

The median to the hypotenuse of a right triangle is half as long as the hypotenuse.

Front 174

Theorem 9-27 The 30-60-90 Triangle Theorem

Back 174

If an acute angle of a right triangle has measure 30, then the pposite side is half as long as the hypotenuse

Front 175

Theorem 9-28

Back 175

If one leg of a right triangle is half as long as the hypotenuse, then the opposite angle has measure 30.

Front 176

Definition of intercept on the transversal

Back 176

If a transversal intersects two lines l1, l2 in points A and B, then we say that l1 and l2 intercept the segment AB on the transversal.

Front 177

Theorem 9-29

Back 177

If three parallel lines intercept congruent segments on one transversal T, then they intercept congruent sements on every transversal T1 which is parallel to T.

Front 178

Theorem 9-30

Back 178

If three parallel lines intercept congruent segments on one transversal then they intercept congruent segments on any other transversal

Front 179

Corollary 9-20.1

Back 179

If three or more parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any othet transversal.

Front 180

Definition of point of concurrency

Back 180

Two or more lines are concurrent if there is a single point which lies on all of them. The common point is called the point of concurrency.

Front 181

Theorem 9-31 The Median Concurrence theorem

Back 181

The medians of every triangle are concurrent. Their point of concurrency is two-thirds of the way along each median, t