# geo postulates theorems

 Through any two points there is exactly one line postulate through any three noncollinear points there is exactly one plane containing them postulate If two points lie in a plane, then the line containing those points lies in the plane postulate if two lines intersect, then they intersect in exactly one point postulate if two planes intersect, then they intersect in exactly one line postulate the points on a line can be put into a one-to-one correspondence with the real numbers ruler postulate If B is between A and C, then AB+BC=AC Segment Addition Postulate given line AB and a point O on line AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180 protractor postulate help classify angles by their measure If S is in the interior of q is a true statement and p is true, then q is true law of detachment if p --> and q --> r are true statements, then p --> r is a true statement law of syllogism addition property of equality if a=b, then a+c=b+c subtraction property of equality if a=b, then a-c =b-c multiplication property of equality if a=b, then ac=bc division property of equality if a=b, and c DOES NOT = 0, then a/c = b/c reflexive property of equality a=a duhhh symmetric property of equality if a=b then b=a transitive property of equality if a=b and b=c, then a=c substitution property of equality if a=b, then b can be substituted for a in any expression reflexive property of congruence figure a ~= figure a line EF =~ line EF Reflex. Prop. of =~ Symmetric property of congruence if figure a ~= figure B, then figure B ~= figure A sym. prop. of ~= Transitive Property of Congruence If figure A~= figure B and figure B ~= figure C, than figure A~= figure C trans. prop. of ~= linear pair theorem if two angles form a linear pair, then they are supplementary. hypothesis: right <'s hypothesis: <1~= <2 <1 and <2 are supplementary conclusion: <1 and <2 are right angles corresponding angles postulate if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent alternate interior angles theorem if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent alternate exterior angles theorem if 2 || lines are cut by a transversal, then the pairs of alternate exterior angles are congruent same-side interior angles theorem if 2 || lines are cut by a transversal, then the 2 pairs of same-side interior angles are supplementary converse of the corresponding angles postulate if 2 coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the 2 lines = || Hypothesis: <1 ~= <2 conclusion: m || n parallel postulate through a point P not on line l, there is exactly one line parallel to l converse of the alternate interior angles theorem if 2 coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the 2 lines are parallel converse of the alternate exterior angles theorem if 2 coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the 2 lines are parallel converse of the same side interior angles theorem if 2 coplanar lines are cut by a transversal so that a pair of same side interior angles are supplementary, the the 2 lines are parallel 2 intersecting lines form a linear pair of congruent angles --> the lines are perpendicular theorem conclusion: l is perpendicular to m perpendicular transversal theorem in a plane, if a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other line hypothesis: transversal perpendicular to one parallel line conclusion: transversal perpendicular to the other parallel line 2 lines perpendicular to the same line --> the 2 lines are || theorem parallel lines theorem in a coordinate plane, 2 nonvertical lines are parallel iff they have the same slope. any 2 vertical lines are parallel perpendicular lines theorem in a coordinate plane, 2 non vertical lines are perpendicular iff the product of their slopes is -1 vertical and horizontal lines are perpendicular triangle sum theorem the sum of the angle measures of a triangle is 180 degrees the acute angles of a right triangle are complementary corollary the measure of each angle of an equiangular triangle is 60 degrees corollary m third pair of angles are congruent side side side (SSS) congruence postulate if 3 sides of 1 triangle are congruent to 3 sides of another triangle, then the triangles are congruent side angle side (SAS) congruence if 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of another triangle --> the triangles are congruent angle side angle (ASA) congruence 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another triangle --> congruent triangles angle angle side (AAS) congruence theorem 2 angles and non included side of 1 triangle are ~= to the corresponding angles and non included side of another triangle --> triangles are congruent Hypotenuse-leg (HL) congruence the hypotenuse and a leg of a right triangle are ~= to the hypotenuse and a leg of another right triangle --> the triangles are congruent CPCTC corresponding parts of congruent triangles are congruent isosceles triangle theorem 2 sides of a triangle are congruent --> angles opposite those angles are congruent equilateral triangle corollary if a triangle is equilateral --> it's equiangular equiangular triangle corollary equiangular triangle --> equilateral triangle perpendicular bisector theorem point is on the perpendicular bisector of a segment --> it is equidistant from the endpoints of the segment converse of the perpendicular bisector theorem a point is equidistant from the endpoints of a segment ---> perpendicular bisector of the segment angle bisector theorem if a point is on the bisector of an angle --> equidistant from the sides of the angle converse of the angle bisector theorem if a point in the interior of an angle is equidistant from the sides of the angle --> on the bisector of the angle circumcenter theorem the circumcenter of a triangle is equidistant from the vertices of the triangle can be inside the triangle, outside the triangle, or on the triangle incenter theorem the incenter of a triangle is equidistant from the sides of the triangle centroid theorem the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side triangle midsegment theorem a midsegment of a triangle is || to a side of the triangle, and it's length is half the length of that side. if 2 sides of a triangle are not congruent --> larger angle is opposite the longer side theorem in triangle, the longer side is oposite the larger angle theorem triangle inequality theorem the sum of any 2 side lengths of a triangle is greater than the 3rd side length Authormandyg233 ID61795 Card Setgeo postulates theorems Descriptionno description. im most likely going to still fail. Updated2011-01-25T06:36:44Z Show Answers