Geometry

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pinkprincess325  on June 26, 2012

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Geometry

 Convex Polygona polygon such that no side extended cuts any other side or vertex
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Definitions

Convex Polygon a polygon such that no side extended cuts any other side or vertex
Concave Polygon A polygon that has at least one diagonal with points outside the polygon
Conditional Statement a type of logical statement that has two parts, a hypothesis and a conclusion
Converse Statement a statement that reverses the subject and predicate
Inverse Statement negate both the hypothesis and the conclusion
Contra-positive statement switch and negate the hypothesis and the conclusion; assuming the original statement is true, this statement is always true too
If-Then form The form of a conditional statement that uses the words "if" and "then." The "if" part contains the hypothesis and the "then" part contains the conclusion.
Bi-conditional Statement A statement that contains the phrase "if and only if"
Laws of Detachment If the hypothesis of a true conditional statement is true, then the conclusion is also true.
Law of Syllogism if p ➡q and q➡r are true conditional statements then p➡r is true
Addition Property of Equality if you add the same number to each side of an equation, the two sides remain equal
Multiplication Property of Equality The property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution
Division Property of Equality If you divide each side of an equation by the same nonzero number, the two sides remain equal
Substitution Property of Equality If a=b, then b can be substituted for a in any equation
Distributive Property of Equality a(b+c)=ab+ac
Reflexive Property of Equality For any real number a, a=a
Symmetric Property of Equality If a = b, then b = a
Transitive Property of Equality If a = b and b = c, then a = c
Ruler Postulate The points on a line can be numbered so that positive number differences measure distances.
Segment Addition Postulate If B is between A and C, then AB+BC=AC
Protractor Postulate the rays in a half-rotation can be numbered from 0 to 180 so that positive number differences measure angles
Congruence of Segments segment congruence is reflexive, symmetric, and transitive
Congruence of Angles angle congruence is reflexive, symmetric, and transitive
Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line
Transversal a line that intersects two or more coplanar lines at different points
Alternate Interior Angles Theorem if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Alternate Exterior Angels Theorem if two parallel lines are cut by a transversal, then alternate exterior angles are congruent
Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
Corresponding Angles Converse if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel

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