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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 |
Created by:
Olivia250
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