# geometry FINALS

 a rule that is accepted without proof postulate/axiom the real number that corresponds to a point coordinate the absolute value of the difference of the coordinates of A & B distance two angles that share a common vertex & side but have no common interior points adjacent angles two adjacent angles whose noncommon sides are opposite rays. linear pair two angles whose sides form two pairs of opposite rays vertical angles a closed plane figure polygon in a polygon if no line that contains a side of the polygon contains a point in the interior of the polygon convex a polygon that is not conves concave the distance around a fugure perimeter the distance around a circle circumference the amount of surface covered by a figure area an unproven statement based on observations conjecture find a pattern in specific cases & then write a conjecture for the general case inductive reasoning a specific case for which the conjecture is false counterexample a logical statement that has 2 parts a hypothesis & a conclusion conditional statement a statement that is the opposite of the original statement negation uses facts definitions accepted properties & laws of logic deductive reasoning a = b, then a + c = b + c addition prop a = b then a - c = b - c subtraction prop a=b & c does not = 0 then a/c = b/c division prop a = b ac=bc multiplication prop a logical arguement that shows a statement is true. proof has numbered statements & corresponding reasons two-column proof a statement that can be proven theorem all right angles are congruent right angles congruence theorem if two angles are supplementary to the same angle (or to congruent angles) then they are congurent congruent supplements theoremsame for complements if two angles form a linear pair then they are supplementary LINEAR PAIR POSTULATE vertical angles are congruent vertical angles congruence theorem two lines that do not intersect & are coplanar parllel lines two lines that do not intersect & are not coplanar skew lines is there if a line and a point not on the line, then there if exactly one line through the point parallel to the given line parallel postulate if there is a line & a point not on the line, then there is exactly one line through the point perpendicular to the given line perpendicular postulate a line that intersects two or more coplanar lines & different points transversal if two lines are parallel to the same line, then they are parallel to each other transitive property of parallel lines in a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope slopes of parallel lines two nonvertical lines are perpendicular if & only if the product of their slopes id -1 slopes of perpendicular lines if a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other perpendicular transversal theorem in a plane if two lines are perpendicular to the same line, then they are parallel to each other lines perpendicular to a transversal theorem the original angles interior angles the angles that form linear pairs w/ the interior angles are the exterior angles the sum of the measures of the interior angles of a triangle is 180 triangle sum theorem the measure of an exterior angle of a triangle is = tot he sum of the measures of the two nonadjacent interior angles exterior angle theorem a statement that can be proved easily using the theorem corollary to a theorem the acute angles of a right angle are complementary corollary to the triangle sum theorem if two angles of one triangle are congruent to two angles of another triangle, then the 3rd angles are also congruent third angles theorem if two sides of a triangle are congruent then the angles opposite them are congruent base angles theorem if two angles of a triangle are congruent then the angles opposite them are congruent converse of base angles theorem if a triangle if equilateral then it is equiangular corollary to the base angles theorem if a triangle is equiangular, then it is equilateral corollary to the converse of base angles theorem an operation that moves or changes a geometric figure in some way to produce a new figure transformation the new figure image moves every point of a figure the same direction & distance translation uses a line of reflection to create a mirror image of the original figure reflection turns a fig. around a fixed point rotation a segment that connects the midpoints of two sides of the triangle midpoint of the triangle the segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side & is half as long as that side midsegment theorem a seg., ray, line, or plane that is perpendicular to a segment @ its midpoint perpendicular bisector same distance form each point equidistant in a plane if a point is on the perpendicular bisector of a seg. then it is equidistant from the endpoints of the seg. perpendicular bisector theorm in a plane if a point is equidistant from the endpoints of a seg. then it is on the perpendicular bisector of the segment converse of the perpendicular bisector theorem when three or more lines,rays, or segs. intersect in the same point concurrentthe point is the point of concurrency the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle concurrency of perpendicular bisectors of a triangle the point of concurrency of the 3 perpendicular bisectors circumcenter if a point is on the bisector of an angle, then it is equidistant form the two sides of the angle angle bisector theorem if a point is in the interior of an angle & is equidistant from the sides of the angle then it lies on the bisector of the angle converse of the angle bisector theorem the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle concurrency of angle bisectors of a triangle the point of concurrency of the 3 angle bisectors of a triangle incenter a segment from a vertex to the midpoint of the opposite side. median of triangle point of concurrency of the medians of a triangle centroid the medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. concurrency of medians of a triangle the perpendicular segment from vertex to the opposite side or line that contains the opposite side altitude of a triangle the lines containing the altitudes of a triangle are concurrent concurrency of altitudes of a triangle the point of concurrency for ltitudes orthocenter the sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side triangle inequality theorem if two sides of one triangle are congruent to two sides of another triangle & the includes angle of the 1st is larger than the included angle of the 2nd then the third side of the 1st is longer then the 3rd of the second hinge theorem if two sides of one triangle are congruent to two sides of another triangle & the third side of the first is longer than the third side of the second then the included angle of the first is larger than the included angle of the second converse of the hinge theorem Authorbrendabelle ID55351 Card Setgeometry FINALS Descriptionfinals Updated2010-12-12T22:14:30Z Show Answers