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| Front-side | Reverse-side |
|---|---|
| acute angle | any angle measring between 0 degrees and 90 degrees |
| adjacent angles | two angles sharing a commen vertex and side, but has no commen interior points |
| angle | consists of two different rays that have the same initial point |
| angle addition postulate | if C is in the interior of angle AOD, then m of angle AOC+m of angle COD=m of angle AOD |
| angle bisector | a ray that divides the angle into two congruent angles |
| collinear | points, segments, or rays that lie om the same line |
| complementary angles | the sum of two angle measures is 90 degrees (each angle is the complement of the other) |
| congruent angles | two angles with the same measure |
| congruent segments | two segments with the same length |
| distance formula | square root of (x2-x1) squared + (y2-y1) squared |
| exterior of an angle | the angle between any side of a shape and a line extended from the next side |
| interior of an angle | the area between the rays that make up an angle, and extending away from the vertex to infinity |
| intersecting lines | coplaner lines that have exactly one point in common |
| line segment | a segment of a number line where both endpoints stop the line from continueing in either direction (no arrowheads) |
| linear pair | two adjacent angles whoses noncommen sides are opposite rays |
| Linear pair postulate | if two angles form a linear pair, then they are supplementary (ie. the sun of their measures is 180 degrees) |
| midpoint | bisects the segment into two shorter segments of equal length |
| midpoint | the point that divides the segment into two congruent segments |
| midpoint formula | (x1+x2 , y1+y2) 2 2 |
| oblique lines | lines are oblique if they intersect and do not form right angles |
| obtuse angle | any angle measuring between 90 degrees and 180 degrees |
| opposite rays | if a letter© is between the two endpoints (A, B), than ray CA and ray CB are opposite |
| parallel lines | coplaner lines that don’t intersect |
| perpendicular lines | two lines that intersect to form a right angle a line is perpendicular to a plane if it is perpendicular to each line in the plane that intersects it |
| Point, Line, and Plane Postulates Postulate 10 |
if two distinct planes intersect, then their intersection is a line |
| Point, Line, and Plane Postulates Postulate 5 |
through any two distinct points there exists exactly one line |
| Point, Line, and Plane Postulates Postulate 6 |
a line contains at least two points |
| Point, Line, and Plane Postulates Postulate 7 |
through any three noncollinear points there exists exactly one plane |
| Point, Line, and Plane Postulates Postulate 8 |
a plane contains at least three noncollinear points |
| Point, Line, and Plane Postulates Postulate 9 |
if two distinct points lie in a plane, then the line containing them lies in the plane |
| postulate 12 | if two distinct lines intersect, then their intersection is exactly one point |
| postulate 13-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 |
| postulate 14-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 |
| Properties of Congruence Reflexive Property |
any geometric object is congruent to its self |
| Properties of Congruence Symmetric Property |
if one geometric object is congruent to a second, then the second object is congruent to the first. |
| Properties of Congruence Transitive Property |
if one geometric object is congruent to a second, and the second is congruent to a third, then the first object is congruent to the third object |
| Properties of Equality (a, b, c are real numbers) Addition Property |
if a=b, then a+c=b+c |
| Properties of Equality (a, b, c are real numbers) Division Property |
if a=b and c doesn’t =0, then a/c=b/c |
| Properties of Equality (a, b, c are real numbers) Multiplication Property |
if a=b, then ac=bc |
| Properties of Equality (a, b, c are real numbers) Subtraction Property |
if a=b, then a-c=b-c |
| Properties of Equality (let a, b, c be real numbers) Reflexive Property |
for ant real number a, a=a |
| Properties of Equality (let a, b, c be real numbers) Sustitution Property |
if a=b, then a may be substituted for b in any equation or expression |
| Properties of Equality (let a, b, c be real numbers) Symmetric Property |
if a=b, then b=a |
| Properties of Equality (let a, b, c be real numbers) Transitive Property |
if a=b and b=c, then a=c |
| ray | a segment of a number line where one side has no arrowhead, and the other continues on forever. |
| right angle | any angle equaling 90 degrees |
| segment addition postulate | if B is between A and C, then AB+BC=AC |
| segment bisector | a segmens, ray, line, or plane that intersects a segment at its midpoint |
| skew lines | two lines that don’t lie on the same plane |
| straight angle | any angle equaling 180 degrees |
| supplementary angles | the sum of two angles measures is 180 degrees (each angle is the supplement of the other) |
| Thm 2.1; Congruent supplements thm | if two angles are supplementary to the same angle or to congruent angles, then they are congruent |
| thm 2.2; congruent complements thm | if two angles are complementary to the same angle or to congruent angles, then they are congruent |
| thm 2.3; vertical angles thm | if two angles are vertical angles, then they are congruent |
| thm 3.1; transitivity of parallel lines | if two lines are parrallel to the same line, then they are parallel to each other |
| thm 3.2; property of perpendicular lines | if two coplaner lines are perpendicular to the same line, then they are parallel to each other |
| thm 3.3 | if two lines are perpendicular, then they intersect to form four right angles |
| thm 3.4 | all right angles are congruent |
| thm 3.5 | if two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular |
| transversal | a line that intersects two or more coplaner lines at different points |
| vertical angles | two angles whose sides form two pairs of opposite rays |