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

1107346046	Point	Location in Space	1
1107346047	Line	A series of all point continuing infinitely in opposite directions	2
1107346048	Plane	A flat surface continuing infinitely in all directions of the plane	3
1107346049	Collinear	Existing on the same line	4
1107346050	Coplaner	Existing on the same plane	5
1107346051	Postulate	an accepted statement of fact	6
1107346052	Postulate 1-1	Through any 2 points, there is EXACTLY one line.	7
1107346053	Postulate 1-2	If 2 lines intersect, then they intersect at EXACTLY one point.	8
1107346054	Postulate 1-3	If 2 planes intersect, then they intersect at EXACTLY on line.	9
1107346055	Postulate 1-4	Through any 3 non-collinear points, there is EXACTLY one plane.	10
1107346056	Segment	A series of all point continuing in opposite directions between 2 inclusive endpoints	11
1107346057	Ray	A series of all points continuing infinitely in ONE direction from one inclusive endpoint	12
1107346058	Parallel Lines	Coplaner lines that do not intersect	13
1107346059	Skew Lines	Non-Coplaner lines	14
1107346060	Opposite Rays	Collinear rays with a common endpoint	15
1107346061	Postulate 1-5	AB means "the length of segment ab"	16
1107346062	Postulate 1-6: Segment Addition Postulate	If a, b, and c, are collinear and b is between a and c, then AB+BC=AC	17
1107346063	Congruent	Having equal measure	18
1107346064	Bisector of a Segment	A point, line, ray, or segment that splits a segment into 2 congruent segments	19
1107346065	Midpoint	A point that bisects a segment	20
1107346066	Angles	Formed my 2 rays with a common endpoint (vertex)	21
1107346067	Acute Angle	An Angle whose measure is less than 90 degrees	22
1107346068	Right Angle	An angle whose measure is EXACTLY 90 degrees	23
1107346069	Obtuse Angle	An angle whose measure is great than 90 degrees	24
1107346070	Straight Angle	An angle whose measure is EXACTLY 180 degrees	25
1107346071	Postulate 1-8: Angle Addition Postulate	On 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 AOC	26
1107346072	Straight Angle Corollary to Angle Addition Postulate	If angle AOC is a straight angle, then the measure of angle AOB+the measure of angle BOC=180 degrees	27
1107346073	Perpendicular Lines	2 lines that intersect to form right angles	28
1107346074	Perpendicular Bisector of a Segment	A line, ray, or segment, that intersects a segment at its midpoint to form Right angles	29
1107346075	Angle Bisector	A line or ray that divides and angle into 2 congruent, COPLANER angles	30
1107346076	Distance Formula	d=√[(x₂-x₁)²+(y₂-y₁)²]	31
1107346077	Midpoint Formula	(x₁+x₂)/2, (y₁+y₂)/2	32
1107346078	Perimeter	The sum of the measures of the sides of a polygon	33
1107346079	Polygon	A closed, plane figure, with at least 3 sides that are segments, that intersect only at their endpoints, where no two adjacent sides are collinear	34
1107346080	Circumference	Distance travelled along a circle starting @ 1 point, continuing in one direction, and returning to the original endpoint	35
1107346081	Circumference Formula	c=2∏r	36
1107346082	Formula for Area of a Circle	a=∏r²	37
1107346083	Area	The number of square units that a figure encloses	38
1107346084	Postulate 1-10	The area of a figure is equal to the sum of the areas of its non-overlapping parts.	39
1107346085	Postulate 1-9	If 2 figures are congruent, then their areas are equal	40
1107346086	Conditional Statements	If____, then ____, p→q	41
1107346087	Law of Syllogism	If p→q, and q→r, then p→r	42
1107346088	Law of Detachment	If p→q and p is true, then q is true	43
1107346089	Biconditional Statement	Can be written iff (if and only if) both the conditional and the converse are true	44
1107346090	Properties of Equality	Addition, Subtraction, Multiplication, Division, Reflexive, Symmetric, Transitive, Substitution, Distributive	45
1107346091	Properties of Congruency	Transitive, Reflexive, Symmetric	46
1107346092	Vertical Angle Theorem	Vertical angles are congruent	47
1107346093	Vertical Angles	Angles formed by 2 sets of opposite rays	48
1107346094	Adjacent Angles	Coplaner angles with a common side, common vertex, and no common interior points	49
1107346095	Supplementary Angles	2 Angles whose measures add up to 180 degrees	50
1107346096	Complementary Angles	Angles whose measures add up to 90 degrees	51
1107346097	Theorem 2-2: Congruent Supplements Theorem	If 2 angles are supplementary to the same angle (someone please fill in these parentheses), then they are congruent to each other	52
1107346098	Theorem 2-3: Congruent Complements Theorem	If 2 angles are complementary to the same angle, then they are congruent to each other	53
1107346099	Quadratic Formula	x=[(-b)±√(b²-4ac)]/2a	54
1107346100	Theorem 2-4: Right Angle Congruency Theorem	If angles are right angles, then they are congruent.	55
1107346101	Theorem 2-5	If two angles are both supplementary and congruent, then they are both right angles.	56
1107346102	Transversal	A line that intersects 2 coplaner lines at two distinct points	57
1107346103	Corresponding Angles Postulate	If a transversal intersects parallel lines, then corresponding angles are congruent.	58
1107346104	Alternate Interior Angles Theorem (AIA Th.)	If a transversal intersects parallel lines, then the alternate interior angles are congruent.	59
1107346105	Same-Side Interior Angles Theorem (SSIA Th.)	If a transversal intersects parallel lines, then the same-side interior angles are supplementary.	60
1107346106	Theorem 3-5	If 2 lines are parallel to the same line, then those two lines are parallel to each other.	61
1107346107	Theorem 3-6	In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.	62
1107346108	Postulate 3-2: Converse to Corresponding Angles Postulate	If corresponding angles are congruent, then a transversal intersects parallel lines.	63
1107346109	Theorem 3-3: Converse to AIA Th.	If alternate interior angles are congruent, then a transversal intersects parallel lines.	64
1107346110	Theorem 3-4: Converse to SSIA Th.	If same-side interior angles are supplementary, then a transversal intersects parallel lines.	65
1107346111	Theorem 3-7 Triangle Angle Sum Theorem	The sum of the measures of the interior angles of a triangle is 180 degrees.	66
1107346112	Theorem 3-8: Triangle Exterior Angle Theorem	The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.	67
1107346113	Exterior Angle of a Polygon	Formed by extending ONLY ONE side of a polygon at a given vertex	68
1107346114	Remote Interior Angles	Non-adjacent interior angles	69
1107346115	Equiangular Triangle	A triangle with 3 congruent angles	70
1107346116	Right Triangle	A triangle with 1 Right angle	71
1107346117	Acute Triangle	A triangle with 3 acute angles	72
1107346118	Obtuse Triangle	A triangle with 1 obtuse angle	73
1107346119	Equilateral Triangle	A triangle with 3 congruent sides	74
1107346120	Isosceles Triangle	A triangle with AT LEAST 2 congruent sides	75
1107346121	Scalene Triangle	A triangle with no congruent sides	76
1107346122	Diagonal	A segment whose endpoints are NON-ADJACENT vertexes of a polygon	77
1107346123	Theorem 3-4: Polygon Sum Theorem	The sum of the measures of the interior angles of an n-sided polygon=(n-2)180 When n≥3	78
1107346124	Concave Polygon	Formed when a single point from any diagonal is in the exterior of the polygon	79
1107346125	Theorem 3-10: Polygon Exterior Angle Theorem	The sum of the measures of the exterior angles of ANY polygon=360 degrees.	80