## Geometry H - Schwarz

##### Created by:

ktoepel  on September 14, 2011

##### Classes:

Geometry H, Schwarz

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# Geometry H - Schwarz

 Positive conditional statementIf p --> then q
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#### 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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