Geometry H - Schwarz
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42 terms
Terms | Definitions |
|---|---|
 Positive conditional statement | If p --> then q |
| Inverse conditional statement | If not p --> then not q |
| Converse conditional sratement | If q --> then p |
| Contrapositive conditional statement | If not q --> then not p |
| Biconditional statement | Contains the phrase "if and only if" |
| Law of Syllogism | If p-->q is a true conditional statement and p is true, then q is true |
| Definition of Congruence | = <--> congruent |
| Definition of Right Angles | right angle ==> 90* 90* ==> right angle |
| Definition of Bisectors | bisected <--> 2 congruent parts |
| Definition of Complementary Angles | comp <--> sum = 90 |
| Definition of Supplementary Angles | supp <--> sum = 180 |
| Definition of Perpendicularity | perpendicular <--> right angle |
| Definition of Midpoint | midpoint <--> 2 congruent parts |
| Definition of Linear Pair | <1 and <2 are a linear pair |
| Definition of Vertical Angles | <1 and <2 are vertical angles |
| Segment Addition Postulate (SAP) | AB + BC = AC |
| Angle Addition Postulate (AAP) | <ABC + <CBD = <ABD |
| Line Postulate | 2 points = 1 line |
| Reflexive | a=a |
| Linear Pair Postulate (LPP) | If two angles form a linear pair, then they are supplementary |
| Parallel Postulate | If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line |
| 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 |
| Right Angle Theorem (RAT) | All right angles are congruent |
| Vertical Angle Theorem (VAT) | All vertical angles are congruent |
| Congruent Supplements Theorem | If two angles are supplementary to the same angle (or to congruent angles) then they are congruent ex. If m<1 + m<2 = 180 and m<2 + m<3 = 180, then <1 is congruent to <3 |
| Congruent Complements Theorem | If two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent ex. if m<4 + m<5 = 90 and m<5 + m<6 = 90, then <4 is congruent to <6 |
| Symmetric Property | If a = b, then b = a |
| Transitive Property | If a = b and b = c, then a = c |
| transversal | line that intersects two or more coplanar lines at different points |
| Corresponding Angles Postulate | two angles that occupy corresponding positions are congruent |
| Alternate Exterior Angles Theorem | two angles that lie outside the two lines on opposite sides of the transversal are congruent |
| Alternate Interior Angles Theorem | two angles that lie between the two lines on opposite sides of the transversal are congruent |
| Consecutive Interior Angles Theorem | two angles that lie between the two lines on the same side of the transversal are supplementary |
| Triangle Sum Theorem | The sum of the measures of the angles of a triangle is 180° |
| Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles |
| Transitivity of Parallelism Theorem (Trans of II) | If 2 lines are parallel to the same line, they're parallel to eachother |
| Slopes of parallel lines: | 2 lines are parallel <--> same slope |
| Theorem 3.3 | If 2 lines are perpendicular <--> intersect to form 4 right angles |
| equation of a perpendicular slope | m1 x m2 = -1 |
| standard form of a line | Ax + By = C |
| slope-intercept form | y = mx + b |
| point-slope form | y - y1 = m(x - x1) |
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