Geometry, Angles

Front 1

zero angle

Back 1

m=0°

Front 2

right angle

Back 2

m=90°

Front 3

obtuse angle

Back 3

90°<m<180°

Front 4

straight angle

Back 4

m=180°

Front 5

complementary angles

Back 5

sum of two angles = 90°

Front 6

supplementary angles

Back 6

sum of two angles = 180°

Front 7

adjacent angles

Back 7

two angles that share a side

Front 8

linear pair of angles

Back 8

adjacent angles with non-common sides forming a line (are opposite rays)

Front 9

vertical angles

Back 9

two non-straight angles are vertical angles iff the union of their sides is two straight lines (angles form an X)

Front 10

perpendicular

Back 10

2 segments, rays or lines are perpendicular iff the lines containing them form a right angle

Front 11

2 perpendicular line theorem

Back 11

If 2 co-planar lines l and m are each perpendicular to the same line, p, they are parallel to each other.

Front 12

Perpendicular to parallel line theorem

Back 12

If a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

Front 13

Perpendicular lines and slopes theorem

Back 13

Two non-vertical lines are perpendicular iff the product of their slopes is -1

Front 14

Transversal

Back 14

2 lines intersected by a third line

Front 15

corresponding angles

Back 15

any pair of angles in similar locations with respect to a transversal

Front 16

corresponding angle postulate

Back 16

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

Front 17

Vertical Angles Theorem

Back 17

If two angles are vertical angles, then they have equal measures

Front 18

Linear Pair Theorem

Back 18

If two angles form a linear pair, then they are supplementary

Front 19

Addition Property of Equality

Back 19

If a = b, then a + c = b + c

Front 20

Reflexive Property of Equality

Back 20

a=a

Front 21

Symmetric Property of Equality

Back 21

If a=b, then b=a

Front 22

Transitive Property of Equality

Back 22

If a=b and b=c, then a=c

Front 23

Multiplication Property of Equality

Back 23

If a=b, then ac=bc

Front 24

Transitive Property of Inequality

Back 24

If a<b and b<c, then a<c

Front 25

Addition Property of Inequality

Back 25

If a<b, then a+c<b+c

Front 26

Multiplication Properties of Inequality

Back 26

If a<b and c>0, then ac<bc.
If a,b and c<0, then ac>bc.

Front 27

Equation to Inequality Property

Back 27

If a and b are positive numbers and a+b=c, then c>a and c>b. (the whole is greater than its parts)

Front 28

Substitution Property

Back 28

If a=b, then a may be substituted for b in any equation.

Front 29

proof argument for a conditional

Back 29

a sequence of justified conclusions, starting with the antecedent (numbered 0) and ending with the consequent. [one step - uses definition or theorem]

Front 30

slope

Back 30

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

Front 31

Parallel lines and Slopes Theorem

Back 31

Two nonvertical lines are parallel iff they have the same slope

Front 32

Transitivity of Parallelism Theorem

Back 32

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