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# Mathematics

### Geometry

Term | Definition |
---|---|

Addition Property of Equality | If a = b, then a + c = b + c |

Subtraction Property of Equality | If a = b, then a - c = b - c |

Division Property of Equality | If a = b, then ac = bc |

Reflexive Property of Equality | a = a |

Symmetric Property of Equality | If a = b, then b = a |

Transitive Property of Equality | If a = b, then b can be substituted for a in any expression. |

Distributive Property of Equality | a( b + c ) = ab + ac |

Reflexive Property of Congruence | Figure a ≅ Figure a |

Transitive Property of Congruence | If figure a ≅ figure b ≅ figure c, then figure a ≅ figure c |

Symmetric Property of Congruence | If figure a ≅ figure b, then figure b ≅ figure a |

Parallel lines | Are coplanar and do not intersect. |

Perpendicular lines | Intersect at a 90° angle. |

Skew lines | Not coplanar and not parallel, do not intersect. |

Parallel planes | Planes that do not intersect. |

Transversal | Is a line that intersects two coplanar lines at two different points. |

Corresponding angles | Lie on the same side fo the transversal ( one on the interior and the other on the exterior). They are congruent. |

Alternate interior angles | Are non adjacent angles that lie on the opposite sides of the transversal. They are congruent. |

Alternate exterior angles | Lie on the opposite side of the transversal. They are congruent |

Same-side interior angles | Lie on the same side of the transversal. and the measure of the angles is equal , add up to 180° |

Corresponding Angle Postulate | If two lines are cut by a transversal, then the pairs of corresponding angles are congruent. |

Alternate interior angles theorem | If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. |

Alternate exterior angles theorem | When two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent . |

Same side interior angles theorem | when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees. |

Parallel Postulate | Through a point p not on line l, there is exactly one line parallel to l |

Converse of the Alternate Interior Angles Theorem | If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel. |

Converse of the Alternate Exterior Angles Theorem | If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then two lines are parallel. |

Converse of the Same-Side Interior Angles Theorem | If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel. |

Converse of the Corresponding Angle Postulate | If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. |

Linear Pair Theorem | If two angles form a linear pair then they are supplementary. |

Parallel lines theorem | In a coordinate plane, two non vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. |

Perpendicular lines theorem | In a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slope is -1. vertical and horizontal lines are perpendicular. |

The Slope of a Line | Is the ratio of the rise to run. If (x1,y1) and (x2 and y2) are any two points of the line, the slope of the line is m= y2 - y1 / x2 - x1. |

Slope | Is a line that describes the steepness of the line. |

Undefined | A fraction with zero as a denominator is undefined because it is impossible to divide a number by zero. |

Positive slope | Line comes from left to right |

Negative slope | Line comes from right to left |

0 slope | Line is horizontal |

VUX HOY | Vertical Undefined X only equation Horizontal 0 zero Y only |

Parallel | Have the same slope but different y intercept |

Coincide | |

Intersect | |

Perpendicular | Opposite in signs, they are recipricles of one another 3 = -3 |

Dilation | (x,y) - (kx, ky) , K> 0 |

Translation | (x,y) - (x + a, y + b) |

Reflection | (x,y) - (-x,y) reflection across y-axis (x,y) - (x,-y) reflection across x- axis |

Rotation | (x,y) - (y,-x) rotation about (0,0) 90° clockwise (x,y) - (-y,x) rotation about (0,0) 90° counter clockwise (x,y) - (-x,-y) rotation about 180° |

Scalene triangles | No sides are equal |

Acute triangles | Three acute angles |

Equiangular triangles | Three congruent acute acute angles |

Right triangle | One right angle |

Obtuse triangle | One obtuse angle |

Equilateral | Three congruent sides |

Scalene | No congruent sides |

Isoceles | Atleast two congruent sides |

SSS | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. |

SAS | If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. |

ASA | |

AAS | |

HL |