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Geometry: Postulates, Theorems, and Corollaries Flashcards

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39259247Post: Segment AdditionIf B is between A and C, then AB + BC = AC0
39259248Post: Angle AdditionIf point B lies in the interior of angle AOC, then m-angle AOB + m-angle BOC = m-angle AOC1
39259249Post 5A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all on one plane2
39259250Post 6Through any two points there is exactly one line3
39259251Post 7Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane4
39259252Post 8If two points are in a plane, then the line that contains the points is in that plane5
39259253Post 9If two planes intersect, then their intersection is a line6
39259254Theo 1-1If two lines intersect, then they intersect in exactly one point7
39259255Theo 1-2Through a line and a point not in the line there is exactly one plane8
39259256Theo 1-3If two lines intersect, then exactly one plane contains the line9
39259257Theo: MidpointIf M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2 AB10
39259258Theo: Angle BisectorIf ray BX bisects angle ABC, then m-angle ABX=1/2 m-angle ABC; m-angle XBC=1/2 m-angle ABC11
39259259Theo 2-3Vertical angles are congruent12
39259260Theo 2-4If two lines are perpendicular, then they form congruent adjacent angles13
39259261Theo 2-5If two lines form congruent adjacent angles, then the lines are perpendicular14
39259262Theo 2-6If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary15
39259263Theo 2-7If the angles are supplements of congruent angles (or of the same angle), then the two angles are congruent16
39259264Theo 2-8If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent17
39259265Theo 3-1If two parallel planes are cut by a third plane, then the lines of intersection are parallel18
39259266Post 10If two parallel lines are cut by a transversal, then corresponding angles are congruent19
39259267Theo 3-2If two parallel lines are cut by a transversal then alternate interior angles are congruent20
39259268Theo 3-3if two parallel lines are cut by a transversal, then same-side interior angles are supplementary21
39259269Theo 3-4If a transversal is perpendicular to one of two parallel lines, then it's perpendicular to the other one also22
39259270Post 11If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel23
39259271Theo 3-5If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel24
39259272Theo 3-6If two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel25
39259273Theo 3-7Any plane, two lines perpendicular to the same line are parallel26
39259274Theo 3-8Through a point outside a line, there is exactly one line parallel to the given line27
39259275Theo 3-9Through a point outside a line there is exactly one line perpendicular to the given line28
39259276Theo 3-10Two lines parallel to a third line are parallel to each other29
39259277Theo 3-11The sum of the measures of the angles of a triangle is 18030
39259278Coro 3-1If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent31
39259279Coro 3-2Each angle of an equiangular triangle has measure 6032
39259280Coro 3-3Any triangle, there can be at most one right angle or obtuse angle33
39259281Coro 3-4Acute angles of a right triangle are complementary34
39259282Theo 3-12The measure of an exterior angle of a triangle equals the sum of the measures of two remote interior angles35
39259283Theo 3-13The sum of the measures of the angles of a convex polygon with N sides is (n-2)18036
39259284Theo 3-14The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 36037
39259285Post: SSSIf three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent38
39259286Post: SASIf two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the triangles are congruent39
39259287Post: ASAIf two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the triangles are congruent40
39674801Theo 4-1If two side of a triangle are congruent, then the angles opposite those sides are congrunet41
39674802Coro 4-1An equilateral triangle is also equiangular42
39674803Coro 4-2An equilateral triangle has three 60 degree angles43
39674804Coro 4-3The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint44
39674805The 4-2If two angles of a triangle are congruent, then the sides opposite those angles are congruent45
39674806Coro 4-4An equiangular triangle is also equilateral46

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