geometry, angles
Terms
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- 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