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