# Shared Flashcard Set

## Details

Geometry - Chapter 1-3
Tehachapi High School Geometry Book
103
Mathematics
10/29/2012

## Additional Mathematics Flashcards

Term
 Space
Definition
 The set of all pointsPg. 6
Term
 Collinear Points
Definition
 Points all in one linePg. 6
Term
 Coplanar Points
Definition
 Points all in one planePg. 6
Term
 Intersection
Definition
 Where two figures(lines, planes, or the combination of both) meet or cut.The set of points that are in both figures. Pg. 6
Term
 Segment
Definition
 Shown by two letters(the endpoints) with a line over it.Constists of the endpoints and all points betweenthose endpoints. Pg. 11
Term
 Ray
Definition
 Shown by two letters(one an endpoint named first and another) with an arrow going to the right over the top.Consists of the endpoint and all points to and paste the second letter. Pg. 11
Term
 Opposite Ray
Definition
 Rays that start at the same endpoint, but go in opposite direction. Pg. 11
Term
 Length
Definition
 Shown by two letters(the endpoints).Subtract the coordinates of it endpoints. Pg. 11
Term
 PostulateAxioms
Definition
 Statements that are accepted wihout proofPg. 12
Term
 Ruler Postulate
Definition
 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinantes 0 and 1.2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates. Pg. 12
Term
Definition
 If B is between A and C, thenAB + BC = ACPG. 12
Term
 Congruent andCongruent Segments
Definition
 Two objects that have the same size and shape.Two segements that have equal length.Pg. 13
Term
 Midpoint of a Segment
Definition
 The point that divides the segment into two congruent segements.Pg. 13
Term
 Bisector of a Segment
Definition
 A line, segment, ray, or plane that intersects the segment at its midpoint.Pg. 13
Term
 Angle
Definition
 The figure formed by two rays that have the same endpoint.Pg. 17
Term
 Sides &Vertex of an angle
Definition
 Sides - the two rays that form the angleVertex - the common endpoint of the rays that form the anglePg. 17
Term
 Acute Angle
Definition
 Measure between o and 90Pg. 17
Term
 Right Angle
Definition
 Measure of 90Pg. 17
Term
 Obtuse Angle
Definition
 Measure between 90 and 180Pg. 17
Term
 Straight Angle
Definition
 Measure of 180Pg. 17
Term
 Protractor Postulate
Definition
 On line AB in a given plane, choose any point 0 between A and B. Consider line OA and line OB and all the rays that can be drawn from o on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: a. Line OA is paired with 0, and line OB with 180.b. If line OB is paired with x, and line OQ with y, then m ‹ POQ = ǀx-yǀ Pg. 18
Term
Definition
 If point B lines in the interior of
Term
 Congruent Angles
Definition
 Angles that have equal measuresPg. 19
Term
Definition
 Two angles in a plane that have a common vertex and a common side but no common interior pointsPg. 19
Term
 Bisector of anAngle
Definition
 The ray that divides that angle inot two congruent adjacent angles.Pg. 19
Term
 Postulate 5# of points in a line
Definition
 A Line contains at least two points; a plane contains at least three points not all in one line; space contaoins at least four points not all in one plane.Pg. 23
Term
 Postulate 6Forming a line
Definition
 Through any two points there is exactly one line.Pg. 23
Term
 Postulate 7# of points in a plane
Definition
 Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.Pg. 23
Term
 Postulate 8Lines in a plane
Definition
 If two points are in a plane, then the line that contains the points is in that plane.Pg. 23
Term
 Postulate 9Intersecting planes
Definition
 If two planes interest, then their intersection is a line.Pg. 23
Term
 Theorem 1-1Intersecting lines
Definition
 If two lines intersect, then they intersect in exactly one point.Pg. 23
Term
 Theorem 1-2Forming a plane
Definition
 Through a line and a point not in a line there is exactly one plane.Pg. 23
Term
 Theorem 1-3 Intersecting lines and planes
Definition
 If two lines intersect, then exactly one plane contains the lines.Pg. 23
Term
 If-Then StatementsConditional Statements or conditionals
Definition
 Example:If B is bewtween A and C, then AB + AC =ACorIf p, then qPg. 33
Term
 Hypothesis
Definition
 The if part of an if-then statementPg. 33
Term
 Conclusion
Definition
 The then part of an if-then statementPg. 33
Term
 Converse
Definition
 When the hypothesis and conclusion are interchangedPg. 33
Term
 Counterexample
Definition
 When an example can be found where the hypothesis is true and the conclusion is false.Pg. 33
Term
 Biconditional
Definition
 When a conditional and is converse are both true they can be combined into a single statement. A statement that contains the words "if and only if"Pg. 34
Term
Definition
 If a = b and c = d, then a + c = b +dThis can also be used to add a number to both sides.Example: a + 2 = b + 2Pg. 37
Term
 Subtraction Property
Definition
 If a = b and c =d, then a - c = b + dThis can also be used to subtract a number from both sidesExample: a - 2 = b - 2 Pg. 37
Term
 Multiplication Property
Definition
 If a = b and c = d, then a -c = b -dThis can also be used to multiply both sides of the equation by the same number.Example: 1/2a = 1/2bPg. 37
Term
 Division Property
Definition
 If a = b and c ≠ 0, then a/c = b/cPg. 37
Term
 Subsititution Property
Definition
 If a =b, then either a or b may be substituted for the other in any equation (or inequality)Pg. 37
Term
 Reflexive Property
Definition
 a =a or < D ≅ < DPg. 37
Term
 Symmetric Property
Definition
 If a = b, then b = aorIf < D ≅ < E, then < E ≅ < DPg. 37
Term
 Transitive Property
Definition
 If a = b and b = c, then a =corIf < D ≅ < E and < E ≅ < F, the < D ≅ < FPg. 37
Term
 Distributive Property
Definition
 a(d+c) = ad +acPg. 38
Term
 Midpoint Theorem
Definition
 If M is the midpoint of seg AB, then AM = 1/2AB and MB = 1/2ABPg. 43
Term
 Angle BisectorTheorem
Definition
 If Ray BX is the bisector of < ABC, thenm< ABX = 1/2m< ABC and m< XBC = 1/2m< ABCPg. 44
Term
 Reasons Used in Proofs
Definition
 Given InformationDefinitionsPostulatesProperties of Equality or CongruencyTheorems (that have already been proved)Pg. 45
Term
 Complentary Angles
Definition
 Two angles whose measures have the sum of 90Each angle is called a complement of the other.Pg. 50
Term
 Supplementary Angles
Definition
 Two angles whose measures have the sum of 180.Each angle is called asupplement of the other.Pg. 50
Term
 Vertical Angles
Definition
 Two angles that have sides consisting of opposite rays. When two lines interest, they form two pairs of vertical angles.Pg. 51
Term
 Vertical Angle Theorem
Definition
 Vertical angles are CongruentPg. 51
Term
 Theorem 2-4If two lines are ┴, then ___________
Definition
 If two lines are perpendicular, then they form congruent adjacent angles.Pg. 56
Term
 Theorem 2-5If two lines form ≅ adj. <'s, then ________
Definition
 If two lines form congruent adjacent angles, then the lines are perpendicular.Pg. 56
Term
 Theroem 2-6If the ext. sides of two adj. actue <'s are ┴, then ________
Definition
 If the exterior sides of two adjacent acute angles are perpendicular, then the angls are complementary.Pg. 56
Term
 Perpendicular Lines
Definition
 Two lines that intersect to form right angles.Pg. 56
Term
 Theorem 2-7Supplements of ≅ <'s
Definition
 If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.Pg. 61
Term
 Theorem 2-8Complements of ≅ <'s
Definition
 If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.Pg. 61
Term
 Parrallel LinesParrallel Planes
Definition
 Are coplanar lines that do not intersect.Planes that do not intersectPg. 73
Term
 Skew Lines
Definition
 Are noncoplanar lines, that are neither parallel or intersectingPg. 73
Term
 A line and plane are Parallel
Definition
 If they do not intersectPg. 73
Term
 Theorem 3-1If two ǁ planes are cut by a third plane, then _________
Definition
 If two parallel planes are cut by a third plane, then the lines of intersection are parallel.Pg. 74
Term
 Transversal
Definition
 A line that intersects two or more coplanar lines in different points.Pg. 74
Term
 Alternate InteriorAngles
Definition
 Two nonadjacent interior angles on opposite sides of the transversal.Pg. 74
Term
 Same-Side Interior Angles
Definition
 Two interior angles on the same side of the transversal.Pg. 74
Term
 Corresponding Angles
Definition
 Two angles in corresponding positions relative to the two lines.Pg. 74
Term
 Postulate 10Correspoinding <'s
Definition
 If two parallel lines are cut by a transversal, then correspoinding angles are congruent.Pg. 78
Term
 Theorem 3-2Starting with ǁ lines
Definition
 If two parallel lines are cut by a transversal, then alternate interior angles are congruent.Pg. 78
Term
 Theorem 3-3Starting with ǁ lines
Definition
 If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.Pg. 79
Term
 Theorem 3-4If a transversal is ┴ to one of two ǁ lines, then _______
Definition
 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.Pg. 79
Term
 Postulate 11Converse to corr. <'s (Post. 10)
Definition
 If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.Pg. 83
Term
 Theorem 3-5Starting with alt. int. <'s
Definition
 If two lines are cut by a transversal and alt. int. angles are congruent, then the lines are parallel.Pg. 83
Term
 Theorem 3-6Starting with same-side int. <'s
Definition
 If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.Pg. 84
Term
 Theorem 3-7┴ and ǁ lines
Definition
 In a plane two lines are perpendicular to the same line are parallel.Pg. 84
Term
 Theorem 3-8Lines and ǁ's
Definition
 Through a point outside a line, there is exactly one line paralllel to the given line.Pg. 85
Term
 Theorem 3-9Lines and ┴'s
Definition
 Through a point outside a line, there is exactly one line perpendicular to the given line.Pg. 85
Term
 Theorem 3-10Three ǁ lines
Definition
 Two lines parallell to a third line are parallel to each other.Pg. 85
Term
 Ways to ProveTwo Lines Parallel
Definition
 Show corr. <'s are ≅Show alt. int. <'s are ≅Show same-side int. <'s are supp.Show both lines are ┴ to a third lineShow both lines are ǁto a third line.Pg. 85
Term
 Triangle
Definition
 The figure formed by three segments joining three noncollinear points.Pg. 93
Term
 Vertex & Sides of a triangle
Definition
 Vertex - each of the three points of the triangle (Pluural: Vertices)Sides - The segments of a trianglePg. 93
Term
 Scalene Triangle
Definition
 No sides congruentPg. 93
Term
 Isosceles Triangle
Definition
 At least two sides congruentPg. 93
Term
 Equilateral Triangle
Definition
 All sides congruentCan also be considered isoscelesEquilateral triangle is also equiangularPg. 93
Term
 Acute Triangle
Definition
 Three actue <'sPg. 93
Term
 Obtuse Triangle
Definition
 One obtues
Term
 Right Triangle
Definition
 One right
Term
 Equiangular Triangle
Definition
 All <'s congruentEquiangular triangles are also equilaterialPg. 93
Term
 Theorem 3-11Sum of the int. <'s of a ∆
Definition
 The sum of the measure of the angles of a triangle is 180Pg. 94
Term
 Corollary 1, 2, 3 & 4of Theorem 3-11
Definition
 1. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent2. Each angle of an equiangular triangle has measure 603. In a triangle, there can be at most one right angle or obtuse angle4. The acute angles of a right triangle are complementary.Pg. 94
Term
 Theorem 3-12Ext. < of a ∆
Definition
 The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.Pg. 95
Term
 Auxiliary Line
Definition
 A line, ray, or segement added to a diagram to help in a proof.Pg. 94
Term
 Polygon
Definition
 Means "many angles". Any figure with three or more sides having the two qualitiles below.1. Each segment intersects exactly two other segements, one at each endpoint2. No two segments with a common endpoints are collinearPg. 101
Term
 Convex Polygon
Definition
 A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.Pg. 101
Term
 Special Polygons
Definition
 3 Triangle 4 Quadrilateral5 Pentagon 6 Hexagon8 Octagon 10 Decagon n n-gonPg. 101
Term
 Diagonal
Definition
 A segment joining two nonconsecutive vertices of a polygon.Pg. 102
Term
 Theorem 3-13Sum of int. <'s of a polygon
Definition
 The sum of the measures of the angles of a convex polygon with n sides is (n-2)180Pg. 102
Term
 Theorem 3-14Sum of ext. <'s of a polygon
Definition
 The sume of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.Pg. 102
Term
 Regular Polygon
Definition
 A polygon that is both equiangluar and equlateral.Pg. 103
Term
 Deductive Reasoning
Definition
 Conclusion based on accepted statements (definitions, postulates, previous theorems, corolaries, and given information)Conclusion must be true if hypotheses are true.Pg. 106
Term
 Inductive Reasoning
Definition
 Conclusion based on several past observationsConclusion is probably true, but not necessarily true.Pg. 106
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