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32 Cards in this Set

  • Front
  • Back
zero angle
m=0°
right angle
m=90°
obtuse angle
90°<m<180°
straight angle
m=180°
complementary angles
sum of two angles = 90°
supplementary angles
sum of two angles = 180°
adjacent angles
two angles that share a side
linear pair of angles
adjacent angles with non-common sides forming a line (are opposite rays)
vertical angles
two non-straight angles are vertical angles iff the union of their sides is two straight lines (angles form an X)
perpendicular
2 segments, rays or lines are perpendicular iff the lines containing them form a right angle
2 perpendicular line theorem
If 2 co-planar lines l and m are each perpendicular to the same line, p, they are parallel to each other.
Perpendicular to parallel line theorem
If a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.
Perpendicular lines and slopes theorem
Two non-vertical lines are perpendicular iff the product of their slopes is -1
Transversal
2 lines intersected by a third line
corresponding angles
any pair of angles in similar locations with respect to a transversal
corresponding angle postulate
a) if two corresponding angles have the same measure, the lines are parallel
b) if two lines are parallel, then the corresponding angles are congruent
Vertical Angles Theorem
If two angles are vertical angles, then they have equal measures
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary
Addition Property of Equality
If a = b, then a + c = b + c
Reflexive Property of Equality
a=a
Symmetric Property of Equality
If a=b, then b=a
Transitive Property of Equality
If a=b and b=c, then a=c
Multiplication Property of Equality
If a=b, then ac=bc
Transitive Property of Inequality
If a<b and b<c, then a<c
Addition Property of Inequality
If a<b, then a+c<b+c
Multiplication Properties of Inequality
If a<b and c>0, then ac<bc.
If a,b and c<0, then ac>bc.
Equation to Inequality Property
If a and b are positive numbers and a+b=c, then c>a and c>b. (the whole is greater than its parts)
Substitution Property
If a=b, then a may be substituted for b in any equation.
proof argument for a conditional
a sequence of justified conclusions, starting with the antecedent (numbered 0) and ending with the consequent. [one step - uses definition or theorem]
slope
the slope of the line through (x1,y1) and (x2,y2), with x1≠x2, is (y2-y1)/(x2-x1)
[change in y values divided by corresponding change in x values]. Slope of horizontal line =0, slope of vertical line is undefined
Parallel lines and Slopes Theorem
Two nonvertical lines are parallel iff they have the same slope
Transitivity of Parallelism Theorem
In a plance if line l is parallel to line m and line m is parallel to line n, then line l is parallel to line n