Geometry: Postulates, Theorems, and Corollaries Flashcards
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| 39259247 | Post: Segment Addition | If B is between A and C, then AB + BC = AC | 0 | |
| 39259248 | Post: Angle Addition | If point B lies in the interior of angle AOC, then m-angle AOB + m-angle BOC = m-angle AOC | 1 | |
| 39259249 | Post 5 | A 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 plane | 2 | |
| 39259250 | Post 6 | Through any two points there is exactly one line | 3 | |
| 39259251 | Post 7 | Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane | 4 | |
| 39259252 | Post 8 | If two points are in a plane, then the line that contains the points is in that plane | 5 | |
| 39259253 | Post 9 | If two planes intersect, then their intersection is a line | 6 | |
| 39259254 | Theo 1-1 | If two lines intersect, then they intersect in exactly one point | 7 | |
| 39259255 | Theo 1-2 | Through a line and a point not in the line there is exactly one plane | 8 | |
| 39259256 | Theo 1-3 | If two lines intersect, then exactly one plane contains the line | 9 | |
| 39259257 | Theo: Midpoint | If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2 AB | 10 | |
| 39259258 | Theo: Angle Bisector | If ray BX bisects angle ABC, then m-angle ABX=1/2 m-angle ABC; m-angle XBC=1/2 m-angle ABC | 11 | |
| 39259259 | Theo 2-3 | Vertical angles are congruent | 12 | |
| 39259260 | Theo 2-4 | If two lines are perpendicular, then they form congruent adjacent angles | 13 | |
| 39259261 | Theo 2-5 | If two lines form congruent adjacent angles, then the lines are perpendicular | 14 | |
| 39259262 | Theo 2-6 | If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary | 15 | |
| 39259263 | Theo 2-7 | If the angles are supplements of congruent angles (or of the same angle), then the two angles are congruent | 16 | |
| 39259264 | Theo 2-8 | If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent | 17 | |
| 39259265 | Theo 3-1 | If two parallel planes are cut by a third plane, then the lines of intersection are parallel | 18 | |
| 39259266 | Post 10 | If two parallel lines are cut by a transversal, then corresponding angles are congruent | 19 | |
| 39259267 | Theo 3-2 | If two parallel lines are cut by a transversal then alternate interior angles are congruent | 20 | |
| 39259268 | Theo 3-3 | if two parallel lines are cut by a transversal, then same-side interior angles are supplementary | 21 | |
| 39259269 | Theo 3-4 | If a transversal is perpendicular to one of two parallel lines, then it's perpendicular to the other one also | 22 | |
| 39259270 | Post 11 | If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel | 23 | |
| 39259271 | Theo 3-5 | If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel | 24 | |
| 39259272 | Theo 3-6 | If two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel | 25 | |
| 39259273 | Theo 3-7 | Any plane, two lines perpendicular to the same line are parallel | 26 | |
| 39259274 | Theo 3-8 | Through a point outside a line, there is exactly one line parallel to the given line | 27 | |
| 39259275 | Theo 3-9 | Through a point outside a line there is exactly one line perpendicular to the given line | 28 | |
| 39259276 | Theo 3-10 | Two lines parallel to a third line are parallel to each other | 29 | |
| 39259277 | Theo 3-11 | The sum of the measures of the angles of a triangle is 180 | 30 | |
| 39259278 | Coro 3-1 | If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent | 31 | |
| 39259279 | Coro 3-2 | Each angle of an equiangular triangle has measure 60 | 32 | |
| 39259280 | Coro 3-3 | Any triangle, there can be at most one right angle or obtuse angle | 33 | |
| 39259281 | Coro 3-4 | Acute angles of a right triangle are complementary | 34 | |
| 39259282 | Theo 3-12 | The measure of an exterior angle of a triangle equals the sum of the measures of two remote interior angles | 35 | |
| 39259283 | Theo 3-13 | The sum of the measures of the angles of a convex polygon with N sides is (n-2)180 | 36 | |
| 39259284 | Theo 3-14 | The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360 | 37 | |
| 39259285 | Post: SSS | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent | 38 | |
| 39259286 | Post: SAS | If 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 congruent | 39 | |
| 39259287 | Post: ASA | If 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 congruent | 40 | |
| 39674801 | Theo 4-1 | If two side of a triangle are congruent, then the angles opposite those sides are congrunet | 41 | |
| 39674802 | Coro 4-1 | An equilateral triangle is also equiangular | 42 | |
| 39674803 | Coro 4-2 | An equilateral triangle has three 60 degree angles | 43 | |
| 39674804 | Coro 4-3 | The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint | 44 | |
| 39674805 | The 4-2 | If two angles of a triangle are congruent, then the sides opposite those angles are congruent | 45 | |
| 39674806 | Coro 4-4 | An equiangular triangle is also equilateral | 46 |