Geometry
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| Addition Property of Equality | If a = b, then a + c = b + c
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| Subtraction Property of Equality | If a = b, then a - c = b - c
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| Division Property of Equality | If a = b, then ac = bc
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| Reflexive Property of Equality | a = a
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| Symmetric Property of Equality | If a = b, then b = a
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| Transitive Property of Equality | If a = b, then b can be substituted for a in any expression.
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| Distributive Property of Equality | a( b + c ) = ab + ac
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| Reflexive Property of Congruence | Figure a ≅ Figure a
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| Transitive Property of Congruence | If figure a ≅ figure b ≅ figure c, then figure a ≅ figure c
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| Symmetric Property of Congruence | If figure a ≅ figure b, then figure b ≅ figure a
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| Parallel lines | Are coplanar and do not intersect.
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| Perpendicular lines | Intersect at a 90° angle.
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| Skew lines | Not coplanar and not parallel, do not intersect.
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| Parallel planes | Planes that do not intersect.
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| Transversal | Is a line that intersects two coplanar lines at two different points.
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| Corresponding angles | Lie on the same side fo the transversal ( one on the interior and the other on the exterior). They are congruent.
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| Alternate interior angles | Are non adjacent angles that lie on the opposite sides of the transversal. They are congruent.
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| Alternate exterior angles | Lie on the opposite side of the transversal. They are congruent
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| Same-side interior angles | Lie on the same side of the transversal. and the measure of the angles is equal , add up to 180°
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| Corresponding Angle Postulate | If two lines are cut by a transversal, then the pairs of corresponding angles are congruent.
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| Alternate interior angles theorem | If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
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| Alternate exterior angles theorem | When two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent .
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| 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.
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| Parallel Postulate | Through a point p not on line l, there is exactly one line parallel to l
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| 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.
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| 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.
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| 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.
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| 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.
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| Linear Pair Theorem | If two angles form a linear pair then they are supplementary.
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| 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.
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| 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.
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| 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.
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| Slope | Is a line that describes the steepness of the line.
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| Undefined | A fraction with zero as a denominator is undefined because it is impossible to divide a number by zero.
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| Positive slope | Line comes from left to right
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| Negative slope | Line comes from right to left
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| 0 slope | Line is horizontal
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| VUX HOY | Vertical Undefined X only equation
Horizontal 0 zero Y only
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| Parallel | Have the same slope but different y intercept
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| Coincide |
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| Intersect |
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| Perpendicular | Opposite in signs, they are recipricles of one another 3 = -3
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| Dilation | (x,y) - (kx, ky) , K> 0
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| Translation | (x,y) - (x + a, y + b)
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| Reflection | (x,y) - (-x,y) reflection across y-axis
(x,y) - (x,-y) reflection across x- axis
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| 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°
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| Scalene triangles | No sides are equal
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| Acute triangles | Three acute angles
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| Equiangular triangles | Three congruent acute acute angles
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| Right triangle | One right angle
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| Obtuse triangle | One obtuse angle
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| Equilateral | Three congruent sides
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| Scalene | No congruent sides
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| Isoceles | Atleast two congruent sides
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| SSS | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
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| 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.
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| ASA |
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| AAS |
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| HL |
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Created by:
Olivia250
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