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# Mathematics

### Geometry

TermDefinition
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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