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### 60 Cards in this Set

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 The protractor postulate (postulate 9) In a half plane with the edge AB and any point S between A and B, there exists a one-to-one correspondence between the rays that originate at S in that half plane and the real number between 0 and 180. To measure an angle formed by two of these rays, find the absolute value of the difference of the corresponding real numbers. Alternate interior angles a pair of non adjacent angles , both interior, on opposite side of the transversal postulate 5 * If two distinct planes intersect then their intersection is a line unique meaning exactly one or one Linear Pair postulate (postulate 10) If two angles form a linear pair, then they are supplementary angles. parallel planes two planes are parallel iff they do not intersect Postulate 3 * through any two points there are infinitely many planes. * Through any three points there is at least one plane * Through any three noncollinear points there is exactly one plane half plane two halfs of plane that are seperated by a line Concave if any lines of the polygon do contain interior points, the polygon is called concave, polygons a polygon consists of three or more coplaner segments; the segments, sides, intersect only at the endpoints; each endpoint, vertex belongs to exactly two segments; no two segments with a common endpointare collinear Postulate 4 * If two points are in a plane, then the line that contains those points lies entirely in the plane between given three collinear points x,y,z, y is between x and z iff xy+yz=xz postulate 6 * given any two points there is a unique distance between them convex a polygon is convex iff the lines containg teh sides do not contain points in the polygon interior Postulate 1 * a line contains at least two distinct points * A plane contains at least three noncollinear points * Space contains at least four noncollinear points Point has no size or dimension, merely a position indicator. Points are names by upper case letters. regular polygon a polygon is a regular polygon iff it is both equilateral and equilangular parallel segments or rays segments or rays are parallel iff the lines that contain them are parallel Postulate 2 * Two distinct points determine a unique line ray set of points that consists of a segment The Ruler Postulate (postulate 7) There is a one-to-one correspondence between the points of a line and the set of real numbers such that the distance between two distinct points of the line is the absolute valuse of the difference of their coordinates linear pair adjacent angles whose noncommon sides are opposite rays Diagonal a diagonal of a polygon is a segment that joins two nonconsecutive vertices of the polygon. intersection the set of points that lie in both figures postulate 8 * Given any angle there is a unique real number between 0 and 180 known as its degree measure Triangle a set of points is a triangle iff is consists of the figure formed by three segments vonnevting three noncollinear point plane a flat surface with no defined thickness that extends without end in all directions. Usually pictured as a four sided figure. Named with a Capitol letter or with any thre non collinear points. vertical angles two nonadjacent angles formed by two intersecting lines space the set of all points perpendicular bisector of a segment Line, ray segment, or plane that is perpendicular to a segment at its midpoint postulate statement accepted as true interior angles angles inside the lines being transversed Theorem statement that must be proven true scalene no congruent sides segment set of points on a line that consists of two points Supplementary angles Iff their sum=180 line consists of an infinate number of points, and extends in both directions without end. Name lines with 2 points from the line or with a lower case letter. corollary theorem whose justification follows from another theorem measure distance between the endpoints of the segment obtuse triangles one obtuse angle congruent segments having equal measures perpendicular two lines that intersect to form right angles right triangles on right angle auxiliary line lines, segments, rays or points added to a figure in order to facilitate a proof or an understanding of a problem. Their introduction must be justified by a postulate or theorem equilangular three congruent angles equilateral all sides congruent Parallel lines two lines are parallel iff they lie in the same plane and do not intersect bisector any line, segment, ray or plane that intersects a segment at its midpoint exterior angles angles outside the lines being transversed adjacent (next to) have to have a common side, common vertex, no interior points corresponding angles a pair of nonadjacent angles, one interior, one exterior, both on the same side of the transversal skew lines twon lines are skew iff they do not lie in the same plane and do not intersect Complementary angles Iff their sum=90 vertex common endpoints of an angle midpoint point that divides a segment into two congruent segments isosceles two sides congruent acute triangles three acute angles angle the union of two noncollinear rays alternate exterior angles a pair of non adjacent angles, both exterior, on opposite sides of the transversal Tranversal a line is a transversal iff it intersects two or more coplaner lines at different points