Ultimate Geometry (Terms, Postulates, Theorems, etc.) Flashcards

44424072	point	a location (undefined term)	0
44424073	plane	a flat surface made up of points; has no depth and extends indefinitely in all directions (undefined term)	1
44424074	line	made up of points and has no thickness or width (undefined term)	2
44424075	collinear points	points on the same line	3
44424076	axioms/postulates	statements that are accepted without proofs	4
44424077	theorems	statements that can be proven	5
44424078	coplanar	points that lie on the same plane	6
44424079	space	a boundless, three-dimensional set of all points; can contain lines and planes	7
44424080	congruent line segments	two line segments with equal lengths	8
44424081	ray	a type of line that has one endpoint	9
44424082	opposite rays	two rays are opposite to each other iff they have the same endpoint and they are collinear	10
44424083	angle	two rays that share an endpoint	11
44424084	angle bisector	rays, line segments, or lines that divide and angle into two equal parts	12
44424085	complimentary angles	two angles whose measures add up to 90°	13
44424086	supplementary angles	two angles whose measures add up to 180°	14
44424087	90-x	compliment of an angle	15
44424088	180-x	supplement of an angle	16
44424089	adjacent angles	two angles that share a side, share a vertex, and have no common interior point	17
44424090	linear pairs	a pair of adjacent angles whose non-common sides are opposite rays	18
44424091	regular polygon	a polygon where all the sides and angles are congruent	19
44424092	triangle	3 sides	20
44424093	quadrilateral	4 sides	21
44424094	pentagon	5 sides	22
44424095	hexagon	6 sides	23
44424096	heptagon	7 sides	24
44424097	octagon	8 sides	25
44424098	nonagon	9 sides	26
44424099	decagon	10 sides	27
44424100	hendecagon	11 sides	28
44424101	dodecagon	12 sides	29
44424102	conditional statement	a statement that can be written in if-then form	30
44424103	converse	the statement formed by exchanging the hypothesis and conclusion of a conditional statement	31
44424104	inverse	the statement formed by negating both the hypothesis and conclusion of a conditional statement	32
44424105	contrapositive	the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement	33
44424106	symmetric property	if a=b then b=a	34
44424107	skew lines	if two lines are not on the same plane, they cannot intersect	35
44424108	transversal	a line that intersects two (or more) lines at two different points	36
44424109	corresponding angles (postulate)	if two parallel lines are cut by a transversal, then the corresponding angles are congruent	37
44424110	converse of corresponding angles (postulate)	if corresponding angles are congruent, then the lines are parallel	38
44424111	scalene	type of triangle where all sides are different lengths	39
44424112	isosceles	type of triangle where at least two sides have equal lengths	40
44424113	equilateral	type of triangle where all sides are equal in length	41
44424114	acute	type of triangle where all angles are acute	42
44424115	obtuse	type of triangle that contains exactly one obtuse angle	43
44424116	right	type of triangle that contains exactly one right angle	44
44424117	angle sum theorem	given a triangle, the sum of the measures of the interior angles is 180°	45
44424118	alternate interior angle (theorem)	if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent	46
44424119	consecutive interior angle (theorem)	if two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary	47
44424120	alternate exterior angle (theorem)	if two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent	48
44424121	third angle theorem	if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent	49
44424122	exterior angle theorem	the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles	50
44424123	sss	if the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent	51
44424124	sas	if two sides and the included angle of one triangle are congruent to two sides and the included angle another triangle, then the triangles are congruent	52
44424125	asa	if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent	53
44424126	aas	if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent	54
44424127	HL	if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent	55
44424128	isosceles triangle theorem	if two sides of a triangle are congruent, then the angles opposite those sides are congruent	56
44424129	diagonal	a line segment that connects two non-adjacent vertices	57
44424130	CPCTC	corresponding parts of congruent triangles are congruent	58
44424131	perpendicular bisector (of a line segment)	a line that cuts through another line segment at its midpoint and bisects it at a 90° angle	59
44424132	circumcenter	point of concurrency for perpendicular bisectors; equidistant from the vertices	60
44424133	centroid	point of concurrency for medians; 1/3 of the whole	61
44424134	incenter	point of concurrency for angle bisectors; equidistant from each side	62
44424135	orthocenter	point of concurrency for altitudes	63
44424136	right triangle	in what type of triangle is the orthocenter a vertex?	64
44424137	equilateral triangle	in what type of triangle is the orthocenter and circumcenter the same?	65
44424138	never	in what type of triangle is the centroid outside of the triangle?	66
44424139	triangle inequality theorem	in a triangle, the sum of the measures of two sides is greater than the measure of the third side	67
44424140	hinge theorem	if two sides of one triangle are congruent to two sides of another triangle and the included angle in the first triangle is greater than the included angle in the second triangle, then the remaining side of the first triangle is greater than the remaining side of the second triangle	68
44424141	converse of hinge theorem	if two sides of one triangle are congruent to two sides of another triangle and the third side of the first triangle is greater than the third side of the second triangle, then the angle opposite the third side in the first triangle is greater than the angles opposite the third side in the second triangle	69