Math rules for geometry
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Created by:
teamtaub Plus on October 6, 2011
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79 terms
English | Math / Symbols |
|---|---|
 Addition property | if a=b then a+c=b+c |
| Subtraction property | if a=b then a-b=b-c |
| Multiplication property | if a=b then a•c=b•c |
| Division property | if a=b then a/b=b/c |
| reflexive property | a=a |
| symmetric property | if a=b then b=a |
| transitive property | if a=b and b=c then a=c |
| substitution property | if a=b then b can replace a in any expression |
| distributive property | a(b+c)= ab+ac |
| vertical angles | two angles whose sides form two pair of opposite rays |
| adjacent angles | two coplanar angles with a common side, a common vertex, and NO common interior points |
| complementary angles | two angles whose measures have a sum of 90 |
| supplementary | two angles whose measures have a sum of 180 |
| Vertical angle theorem | vertical angles are congruent |
| Congruent supplements theorem | if two angles are supplements of the same angle (or of congruent angles) then the two angles are congruent |
| Congruent complements theorem | if two angles are complements of the same angle (or of congruent angles) then the two angles are congruent right angles are congruent if two angles are congruent and supplementary then each is a right angle |
| congruent angles | angles that have the same measure |
| 2 points postulate | through any two points there is exactly one line |
| 2 lines postulate | if two lines intersect then they intersect in exactly one point |
| 2 planes postulate | if two planes intersect they intersect in exactly one line |
| 3 points postulate | through any 3 noncollinear points there is exactly one plane |
| segment addition postulate | if three points A, B, C are collinear and B is between A and C the AB+BC=AC |
| Angle Addition Postulate | if B is in the interior of <AOC then m<AOB+m<BOC=<AOC if <AOC is a straight angle then <AOB+<BOC=180 |
| acute angle | less than 90 |
| right angle | 90 |
| obtuse angle | more than 90 |
| straight angle | 180 |
| perpendicular lines | 2 lines that intersect to form right angles |
| angle bisector | a ray that divides an angle into two congruent coplanar angles |
| Distance formula | √(x₂-x₁)²+(y₂-y₁)² |
| Midpoint Formula | M= x₁+x₂/2, y₁+y₂/2 |
| transversal | a line that intersects to coplanar lines |
| alternate interior angle | nonadjacent interior angles that lie on opposite sides of the transversal |
| same side interior angles | lie on the same side of the transversal |
| corresponding angles | lie on the same side of the transversal in corresponding positions |
| Corresponding angles postulate | if a transversal intersects two parallel lines then corresponding angles are congruent |
| alternate interior angles theorem | if a transversal intersects two parallel lines then alternate interior angles are congruent |
| same side interior theorem | if a transversal intersects two parallel lines, then same side interior angles are supplementary |
| converse of the corresponding angles postulate | if two line and a transversal form corresponding angles that are congruent, then the two lines are parallel |
| converse of the alternate interior angles theorem | if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel |
| converse of the same side interior angles theorem | if two line and a transversal form same side interior angles that are supplementary then the two lines are parallel |
| parallel lines theorem | if two lines are parallel to the same line then they are parallel to each other |
| perpendicular lines theorem | in a plane if two lines are perpendicular to the same line then they are parallel to each other |
| Triangle angle sum theorem | the sum of the measures of the angles of a triangle is 180 |
| Triangle exterior angle theorem | the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles |
| exterior angles of a polygon | angle formed by a side and an extension of an adjacent side |
| remote interior angles | the 2 angles not near the exterior angle |
| polygon | closed plane figure with at least three sides that are segments |
| convex polygon | has no diagonal with points outside the polygon |
| concave polygon | has at least one diagonal with points outside the polygon |
| polygon angle sum theorem | the sum of the measures of the angles of an n-gon is (n-2)180 |
| polygon exterior angle sum theorem | the sum of the measures of the exterior angles of a polygon one at each vertex is 360 |
| equilateral polygon | all sides are equal |
| equiangular polygon | all angles are equal |
| regular polygon | both angles and sides are equal |
| slope intercept form | y=mx+b |
| standard form | Ax+By=C |
| point-slope form | y-y₁=m(x-x₁) |
| to find slope | y₂-y₁ ______ x₂-x₁ |
| vertical line | x= |
| horizontal line | y= |
| to find y intercept | x=0 |
| to find x intercept | y=0 |
| Quadrilateral | 4 sides |
| Pentagon | 5 sides |
| hexagon | 6 sides |
| heptagon | 7 sides |
| octagon | 8 sides |
| nonagon | 9 sides |
| decagon | 10 sides |
| undecagon | 11 sides |
| dodecagon | 12 sides |
| acute triangle | all of its angles are acute |
| obtuse triangle | has one obtuse angle |
| scalene triangle | no sides or angles congruent |
| right triangle | has a right angle |
| isosceles | at least 2 congruent angles |
| slope of parallel lines | if two non vertical lines are parallel their slopes are equal. |
| slopes of perpendicular lines | if two non vertical lines are perpendicular the product of their slopes is -1 |
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