## Postulates, Properties, Laws, and Definitions in Geometry.

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acairo8  on September 29, 2010

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Okay, so I found this set and it rocked so i copied it

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# Postulates, Properties, Laws, and Definitions in Geometry.

 PointLocation in Space
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#### Definitions

Point Location in Space
Line A series of all point continuing infinitely in opposite directions
Plane A flat surface continuing infinitely in all directions of the plane
Collinear Existing on the same line
Coplaner Existing on the same plane
Postulate an accepted statement of fact
Postulate 1-1 Through any 2 points, there is EXACTLY one line.
Postulate 1-2 If 2 lines intersect, then they intersect at EXACTLY one point.
Postulate 1-3 If 2 planes intersect, then they intersect at EXACTLY on line.
Postulate 1-4 Through any 3 non-collinear points, there is EXACTLY one plane.
Segment A series of all point continuing in opposite directions between 2 inclusive endpoints
Ray A series of all points continuing infinitely in ONE direction from one inclusive endpoint
Parallel Lines Coplaner lines that do not intersect
Skew Lines Non-Coplaner lines
Opposite Rays Collinear rays with a common endpoint
Postulate 1-5 AB means "the length of segment ab"
Postulate 1-6: Segment Addition Postulate If a, b, and c, are collinear and b is between a and c, then AB+BC=AC
Congruent Having equal measure
Bisector of a Segment A point, line, ray, or segment that splits a segment into 2 congruent segments
Midpoint A point that bisects a segment
Angles Formed my 2 rays with a common endpoint (vertex)
Acute Angle An Angle whose measure is less than 90 degrees
Right Angle An angle whose measure is EXACTLY 90 degrees
Obtuse Angle An angle whose measure is great than 90 degrees
Straight Angle An angle whose measure is EXACTLY 180 degrees
Postulate 1-8: Angle Addition Postulate On a plane, if b is in the interior of angle AOC, then the measure of angle AOB+the measure of angle BOC=the measure of angle AOC
Straight Angle Corollary to Angle Addition Postulate If angle AOC is a straight angle, then the measure of angle AOB+the measure of angle BOC=180 degrees
Perpendicular Lines 2 lines that intersect to form right angles
Perpendicular Bisector of a Segment A line, ray, or segment, that intersects a segment at its midpoint to form Right angles
Angle Bisector A line or ray that divides and angle into 2 congruent, COPLANER angles
Distance Formula
d=√[(x₂-x₁)²+(y₂-y₁)²]
Midpoint Formula (x₁+x₂)/2, (y₁+y₂)/2
Perimeter The sum of the measures of the sides of a polygon
Polygon A closed, plane figure, with at least 3 sides that are segments, that intersect only at their endpoints, where no two adjacent sides are collinear
Circumference Distance travelled along a circle starting @ 1 point, continuing in one direction, and returning to the original endpoint
Circumference Formula c=2∏r
Formula for Area of a Circle a=∏r²
Area The number of square units that a figure encloses
Postulate 1-10 The area of a figure is equal to the sum of the areas of its non-overlapping parts.
Postulate 1-9 If 2 figures are congruent, then their areas are equal
Conditional Statements If____, then ____, p→q
Law of Syllogism If p→q, and q→r, then p→r
Law of Detachment If p→q and p is true, then q is true
Biconditional Statement Can be written iff (if and only if) both the conditional and the converse are true
Properties of Equality Addition, Subtraction, Multiplication, Division, Reflexive, Symmetric, Transitive, Substitution, Distributive
Properties of Congruency Transitive, Reflexive, Symmetric
Vertical Angle Theorem Vertical angles are congruent
Vertical Angles Angles formed by 2 sets of opposite rays
Adjacent Angles Coplaner angles with a common side, common vertex, and no common interior points
Supplementary Angles 2 Angles whose measures add up to 180 degrees
Complementary Angles Angles whose measures add up to 90 degrees
Theorem 2-2: Congruent Supplements Theorem If 2 angles are supplementary to the same angle (someone please fill in these parentheses), then they are congruent to each other
Theorem 2-3: Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other
Theorem 2-4: Right Angle Congruency Theorem If angles are right angles, then they are congruent.
Theorem 2-5 If two angles are both supplementary and congruent, then they are both right angles.
Transversal A line that intersects 2 coplaner lines at two distinct points
Corresponding Angles Postulate If a transversal intersects parallel lines, then corresponding angles are congruent.
Alternate Interior Angles Theorem (AIA Th.) If a transversal intersects parallel lines, then the alternate interior angles are congruent.
Same-Side Interior Angles Theorem (SSIA Th.) If a transversal intersects parallel lines, then the same-side interior angles are supplementary.
Theorem 3-5 If 2 lines are parallel to the same line, then those two lines are parallel to each other.
Theorem 3-6 In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.
Postulate 3-2: Converse to Corresponding Angles Postulate If corresponding angles are congruent, then a transversal intersects parallel lines.
Theorem 3-3: Converse to AIA Th. If alternate interior angles are congruent, then a transversal intersects parallel lines.
Theorem 3-4: Converse to SSIA Th. If same-side interior angles are supplementary, then a transversal intersects parallel lines.
Theorem 3-7 Triangle Angle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 degrees.
Theorem 3-8: Triangle Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
Exterior Angle of a Polygon Formed by extending ONLY ONE side of a polygon at a given vertex
Remote Interior Angles Non-adjacent interior angles
Equiangular Triangle A triangle with 3 congruent angles
Right Triangle A triangle with 1 Right angle
Acute Triangle A triangle with 3 acute angles
Obtuse Triangle A triangle with 1 obtuse angle
Equilateral Triangle A triangle with 3 congruent sides
Isosceles Triangle A triangle with AT LEAST 2 congruent sides
Scalene Triangle A triangle with no congruent sides
Diagonal A segment whose endpoints are NON-ADJACENT vertexes of a polygon
Theorem 3-4: Polygon Sum Theorem The sum of the measures of the interior angles of an n-sided polygon=(n-2)180 *When n≥3*
Concave Polygon Formed when a single point from any diagonal is in the exterior of the polygon
Theorem 3-10: Polygon Exterior Angle Theorem The sum of the measures of the exterior angles of ANY polygon=360 degrees.

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