Geometry postulates and theorems from ch 1-4 that we have done so far.
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| 570707266 | segment addition postulate | If B is between A and C, then AB+BC= AC. If AB+BC=AC, then B is between A and C. | 0 | |
| 570707267 | angle addition postulate | If P is in the interior of angle RST, then the measure of angle RST is equal to the sum of the measures of angle RSP and angle PST* | 1 | |
| 570707268 | law of detachment | if the hypothesis of a true conditional statement is true, then the conclusion is also true. | 2 | |
| 570707269 | law of syllogism | if hypothesis p, then conclusion q. if hypothesis q, then conclusion r. if hypothesis p, then conclusion r. | 3 | |
| 570707270 | line postulate | through any two points there exists exactly one line. | 4 | |
| 570707271 | line postulate | A line contains at least two points. | 5 | |
| 570707272 | Intersection of lines postulate | If two lines intersect, then their intersection is exactly one point. | 6 | |
| 570707273 | plane postulate | through any three collinear points there exist exactly one plane. | 7 | |
| 570707274 | points on a plane postulate | if two points lie in a plane, then the line containing then lies in the plane. | 8 | |
| 570707275 | intersection of planes postulate | if two planes intersect, then their intersection is a line. | 9 | |
| 570707276 | line perpendicular to a plane | a line is a line perpendicular to a plane IF AND ONLY IF the line intersects the plane in a point and is perpendicular to every line in a plane that intersects it. | 10 | |
| 570707277 | addition property of equality | if a=b, then a+c=b+c | 11 | |
| 570707278 | subtraction property of equality | if a=b, then a-c=b-c | 12 | |
| 570707279 | multiplication property of equality | if a=b and c does not equal 0, then a/c=b/c | 13 | |
| 570707280 | substitution property | if a=b, then a can be substituted for b in any equation or expression. | 14 | |
| 570707281 | distributive property | a(b+c)=ab=ac, where a,b, and c are real numbers | 15 | |
| 570707282 | reflexive property of equality | REAL NUMBERS: a, a=a. LINE SEGMENTS: AB=AB. ANGLES: m of angle A= m of angle A | 16 | |
| 570707283 | symmetric property of equality | REAL NUMBERS: if a=b, then b=a. 2. LINE SEGMENTS: AB=CD, then CD=AB. ANGLES: if m of angle A=m of angle B, then m of angle B=m of angle B | 17 | |
| 570707284 | transitive property of equality | REAL NUMBERS: if a=b and b=c, then a=c. LINE SEGMENTS: if AB=CD and CD=EF, then AB=EF. ANGLES: if m of angle A=m of angle B and m of angle B=m of angle C, then m of angle A=m of angle C. | 18 | |
| 570707285 | congruence of segments theorem | reflexive, symmetric and transitive | 19 | |
| 570707286 | congruence of angles | reflexive, symmetric and transitive | 20 | |
| 570707287 | right angles congruence theorem | all right angles are congruent | 21 | |
| 570707288 | congruent supplements theorem | if two angles are supplementary to the same angle (or to congruent sides), then they are congruent. | 22 | |
| 570707289 | congruent complements theorem | if two angles are complementary to the same angle (or to congruent angles), then they are congruent. | 23 | |
| 570707290 | linear pair postulate | if two angles form a linear pain, then they are supplementary. | 24 | |
| 570707291 | vertical angles congruence theorem | vertical angles are congruent | 25 | |
| 570707292 | parallel postulate | if there is a line and point not on the line, then there is exactly one line through the point parallel to the given line . | 26 | |
| 570707293 | perpendicular postulate | if there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. | 27 | |
| 570707294 | corresponding angles postulate | if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. | 28 | |
| 570707295 | alternate interior angles theorem | if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. | 29 | |
| 570707296 | alternate exterior angles theorem | if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. | 30 | |
| 570707297 | consecutive interior angles theorem | if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. | 31 | |
| 570707298 | corresponding angles converse | if two parallel lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel. | 32 | |
| 570707299 | alternate interior angles converse | if two parallel lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. | 33 | |
| 570707300 | alternate exterior angles converse | if two parallel lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. | 34 | |
| 570707301 | consecutive interior angle converse | if two parallel lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. | 35 | |
| 570707302 | standard form | Ax+By=C where A and B are not both zero. | 36 | |
| 570707303 | theorem 3.8 (3.6) | if two lines intersect to form a linear pain of congruent angles, then the lines are perpendicular. | 37 | |
| 570707304 | theorem 3.9 (3.6) | if two lines are perpendicular, then they intersect to form four right angles. | 38 | |
| 570707305 | theorem 3.10 (3.6) | if two sides of two adjacent acute angles are perpendicular, then the angles are complementary. | 39 | |
| 570707306 | perpendicular transversal theorem | if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. | 40 | |
| 570707307 | lines perpendicular to a transversal theorem | in a plane, if two lines are perpendicular to the same line, then they are parallel to each other. | 41 | |
| 570707308 | triangle sum theorem | the sum of the measures of the interior angles of a triangle is 180 degrees. | 42 | |
| 570707309 | exterior angle theorem | the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. | 43 | |
| 570707310 | corollary to the triangle sum theorem | the acute angles of a right triangle are complementary. | 44 | |
| 570707311 | triangle congruence postulates | SSS, SAS, ASA, AAS. | 45 | |
| 570707312 | base angles theorem | if two sides of a triangle are congruent, then the angles opposite them are congruent. | 46 | |
| 570707313 | converse of the base angles theorem | if two angles of a triangle are congruent, then the sides opposite them are congruent. | 47 | |
| 570707314 | corollary to the base angles theorem | if a triangle is equilateral, then it is equiangular. | 48 | |
| 570707315 | corollary to the converse of base angles theorem | if a triangle is equiangular, then it is equilateral. | 49 |
