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Postulates, Properties, Laws, and Definitions in Geometry. Flashcards

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1107346046PointLocation in Space1
1107346047LineA series of all point continuing infinitely in opposite directions2
1107346048PlaneA flat surface continuing infinitely in all directions of the plane3
1107346049CollinearExisting on the same line4
1107346050CoplanerExisting on the same plane5
1107346051Postulatean accepted statement of fact6
1107346052Postulate 1-1Through any 2 points, there is EXACTLY one line.7
1107346053Postulate 1-2If 2 lines intersect, then they intersect at EXACTLY one point.8
1107346054Postulate 1-3If 2 planes intersect, then they intersect at EXACTLY on line.9
1107346055Postulate 1-4Through any 3 non-collinear points, there is EXACTLY one plane.10
1107346056SegmentA series of all point continuing in opposite directions between 2 inclusive endpoints11
1107346057RayA series of all points continuing infinitely in ONE direction from one inclusive endpoint12
1107346058Parallel LinesCoplaner lines that do not intersect13
1107346059Skew LinesNon-Coplaner lines14
1107346060Opposite RaysCollinear rays with a common endpoint15
1107346061Postulate 1-5AB means "the length of segment ab"16
1107346062Postulate 1-6: Segment Addition PostulateIf a, b, and c, are collinear and b is between a and c, then AB+BC=AC17
1107346063CongruentHaving equal measure18
1107346064Bisector of a SegmentA point, line, ray, or segment that splits a segment into 2 congruent segments19
1107346065MidpointA point that bisects a segment20
1107346066AnglesFormed my 2 rays with a common endpoint (vertex)21
1107346067Acute AngleAn Angle whose measure is less than 90 degrees22
1107346068Right AngleAn angle whose measure is EXACTLY 90 degrees23
1107346069Obtuse AngleAn angle whose measure is great than 90 degrees24
1107346070Straight AngleAn angle whose measure is EXACTLY 180 degrees25
1107346071Postulate 1-8: Angle Addition PostulateOn a plane, if b is in the interior of angle AOC, then the measure of angle AOB+the measure of angle BOC=the measure of angle AOC26
1107346072Straight Angle Corollary to Angle Addition PostulateIf angle AOC is a straight angle, then the measure of angle AOB+the measure of angle BOC=180 degrees27
1107346073Perpendicular Lines2 lines that intersect to form right angles28
1107346074Perpendicular Bisector of a SegmentA line, ray, or segment, that intersects a segment at its midpoint to form Right angles29
1107346075Angle BisectorA line or ray that divides and angle into 2 congruent, COPLANER angles30
1107346076Distance Formulad=√[(x₂-x₁)²+(y₂-y₁)²]31
1107346077Midpoint Formula(x₁+x₂)/2, (y₁+y₂)/232
1107346078PerimeterThe sum of the measures of the sides of a polygon33
1107346079PolygonA closed, plane figure, with at least 3 sides that are segments, that intersect only at their endpoints, where no two adjacent sides are collinear34
1107346080CircumferenceDistance travelled along a circle starting @ 1 point, continuing in one direction, and returning to the original endpoint35
1107346081Circumference Formulac=2∏r36
1107346082Formula for Area of a Circlea=∏r²37
1107346083AreaThe number of square units that a figure encloses38
1107346084Postulate 1-10The area of a figure is equal to the sum of the areas of its non-overlapping parts.39
1107346085Postulate 1-9If 2 figures are congruent, then their areas are equal40
1107346086Conditional StatementsIf____, then ____, p→q41
1107346087Law of SyllogismIf p→q, and q→r, then p→r42
1107346088Law of DetachmentIf p→q and p is true, then q is true43
1107346089Biconditional StatementCan be written iff (if and only if) both the conditional and the converse are true44
1107346090Properties of EqualityAddition, Subtraction, Multiplication, Division, Reflexive, Symmetric, Transitive, Substitution, Distributive45
1107346091Properties of CongruencyTransitive, Reflexive, Symmetric46
1107346092Vertical Angle TheoremVertical angles are congruent47
1107346093Vertical AnglesAngles formed by 2 sets of opposite rays48
1107346094Adjacent AnglesCoplaner angles with a common side, common vertex, and no common interior points49
1107346095Supplementary Angles2 Angles whose measures add up to 180 degrees50
1107346096Complementary AnglesAngles whose measures add up to 90 degrees51
1107346097Theorem 2-2: Congruent Supplements TheoremIf 2 angles are supplementary to the same angle (someone please fill in these parentheses), then they are congruent to each other52
1107346098Theorem 2-3: Congruent Complements TheoremIf 2 angles are complementary to the same angle, then they are congruent to each other53
1107346099Quadratic Formulax=[(-b)±√(b²-4ac)]/2a54
1107346100Theorem 2-4: Right Angle Congruency TheoremIf angles are right angles, then they are congruent.55
1107346101Theorem 2-5If two angles are both supplementary and congruent, then they are both right angles.56
1107346102TransversalA line that intersects 2 coplaner lines at two distinct points57
1107346103Corresponding Angles PostulateIf a transversal intersects parallel lines, then corresponding angles are congruent.58
1107346104Alternate Interior Angles Theorem (AIA Th.)If a transversal intersects parallel lines, then the alternate interior angles are congruent.59
1107346105Same-Side Interior Angles Theorem (SSIA Th.)If a transversal intersects parallel lines, then the same-side interior angles are supplementary.60
1107346106Theorem 3-5If 2 lines are parallel to the same line, then those two lines are parallel to each other.61
1107346107Theorem 3-6In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.62
1107346108Postulate 3-2: Converse to Corresponding Angles PostulateIf corresponding angles are congruent, then a transversal intersects parallel lines.63
1107346109Theorem 3-3: Converse to AIA Th.If alternate interior angles are congruent, then a transversal intersects parallel lines.64
1107346110Theorem 3-4: Converse to SSIA Th.If same-side interior angles are supplementary, then a transversal intersects parallel lines.65
1107346111Theorem 3-7 Triangle Angle Sum TheoremThe sum of the measures of the interior angles of a triangle is 180 degrees.66
1107346112Theorem 3-8: Triangle Exterior Angle TheoremThe measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.67
1107346113Exterior Angle of a PolygonFormed by extending ONLY ONE side of a polygon at a given vertex68
1107346114Remote Interior AnglesNon-adjacent interior angles69
1107346115Equiangular TriangleA triangle with 3 congruent angles70
1107346116Right TriangleA triangle with 1 Right angle71
1107346117Acute TriangleA triangle with 3 acute angles72
1107346118Obtuse TriangleA triangle with 1 obtuse angle73
1107346119Equilateral TriangleA triangle with 3 congruent sides74
1107346120Isosceles TriangleA triangle with AT LEAST 2 congruent sides75
1107346121Scalene TriangleA triangle with no congruent sides76
1107346122DiagonalA segment whose endpoints are NON-ADJACENT vertexes of a polygon77
1107346123Theorem 3-4: Polygon Sum TheoremThe sum of the measures of the interior angles of an n-sided polygon=(n-2)180 **When n≥3**78
1107346124Concave PolygonFormed when a single point from any diagonal is in the exterior of the polygon79
1107346125Theorem 3-10: Polygon Exterior Angle TheoremThe sum of the measures of the exterior angles of ANY polygon=360 degrees.80

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