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65 Cards in this Set
- Front
- Back
Distance Formula |
D= the square root of (x#2-x#1)^2+(y#2-y#1)^2 which is the Pythagorean formula solved for c |
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Midpoint Formula |
((x#1+x#2)/2 , (y#1+y#2)/2) |
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Adjacent Angles |
two angles that share a side and vertex but do not overlap |
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Linear Pair |
two adjacent angles that form a straight line |
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Definition of Perpendicular |
Lines intersect to form 90* angles |
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Regular Shape |
Equilateral and Equiangular |
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Inductive V. Deductive Reasoning |
Inductive - using observations and patterns to make predictions and conjectures Deductive - drawing logically certain conclusions by using an argument or logic |
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Disjunction |
an "or" statement |
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Logically Equivalent |
two statements that have the same truth value |
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Disjunctive Syllogism (D.S.) |
If one part of an "or" statement is false the other part must be true |
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Law of Syllogism (L.O.S.) |
Given: If A then B, If B then C
Conclusion: If A then C |
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Conditional Statement |
A statement in If-Then form |
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If part of a Conditional Statement |
hypothesis |
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Then part of a Conditional Statement |
conclusion |
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Converse |
formed by switching the hypothesis and conclusion (can be true or false) |
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Inverse |
formed by negating both the hypothesis and the conclusion (can be true or false) |
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Contrapositive |
formed by combining the inverse and converse (same truth value as the original statement) |
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Bi-Conditional Statement |
Contains the phrase "if and only if" (only true if its true both ways) |
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An if-then statement is only false if... |
the hypothesis is true and the conclusion is false (statements are true until proven false) |
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Law of Detachment |
Given: If p then q, p Conclusion: q |
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Postulate V. Theorem |
Postulate - a statement that is accepted as true without proof Theorem - a statement that can be proven true |
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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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Multiplication Property of Equality |
If A=B, then AC = BC |
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Division Property of Equality |
if A=B, then A/C = B/C |
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Symetric |
The order of which things are equal/congruent is insignifigant |
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Definition of Congruent |
used to switch things back and forth between congruent and equal |
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Transitive |
If two things are congruent/equal to the same thing, then they are congruent/equal to each other |
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Substitution |
If A=B, then B can be substituted for A in any equation (Cannot Be Used With Shapes) |
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Segment Addition Postulate |
you can add the lengths of smaller segments together to get bigger ones AB+BC=AC (just pretend like there is segment signs above those segments) |
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Angle Addition Postulate |
m/_ABC+m/_CBD=m/_ABD |
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Linear Pair Postulate |
if two angles form a linear pair, then they are supplementary |
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Congruent Supplements/Complements Theorem |
Two angles that are complementary/supplementary to the same angle are congruent |
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Corresponding Angles Postulate |
if two parallel lines are cut by a transversal, then the corresponding angles are congruent (the converse is also true) |
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Alternate Interior/Exterior Angles Theorem |
if two parallel lines cut by a transversal are parallel, then the alternate interior/exterior angles are congruent (converse is also true) |
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Consecutive Interior Angles Theorem |
if two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary (converse is also true) |
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Parallel Postulate |
Given a line and a point not on the line, there is exactly one line through that point that is parallel to the given line |
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Perpendicular Postulate |
given a line and a point not on that line, there is exactly one line through the point perpendicular to the given point |
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The shortest distance from a point to a line is always... |
...the length of the segment perpendicular to the line from the point 1) find the equation of the line perpendicular through the point 2) find the intersection 3) use the distance formula |
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Triangle Sum Theorem |
The sum of the interior measures of a triangle is 180* |
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Exterior Angle Theorem |
the measure of one exterior angle of a triangle is equal to the sum of the opposing interior angles |
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Corollary |
a statement that follows directly from a theorem |
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Third Angles Theorem |
if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent |
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The Triangle Congruence Postulates that do not exist are |
AAA, ASS, SSA |
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Perpendicular Bisector Theorem |
Any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment (converse is also true)
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Angle Bisector Theorem |
any point on the angle bisector is equidistant from the sides of the angle (converse is also true) |
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Circumcenter |
formed by perpendicular bisectors, equidistant from the vertices |
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Incenter |
formed by the angle bisectors, equidistant from the sides of the triangle |
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Centroid |
formed by medians, center of mass. Distance from midpoint to side is 1/3 the entire median |
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Orthocenter |
formed by altitudes, is useless |
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Indirect Proof |
assume the opposite of what you are trying to prove and show how it is wrong using the words "assume, this is impossible because, therefore" |
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Triangle Inequality Theorem |
the sum of the lengths of any two side lengths is greater than that of the third side |
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Hinge Theorem |
if two triangles have two pairs of congruent sides, then the triangle with the larger included angle has the longer third side |
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Sum of the Interior angles of a polygon with n sides |
(n-2)180 |
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the measure of one interior angle of a regular polygon |
((n-2)180)/n |
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the sum of the exterior angles of a regular polygon is always... |
360 |
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the measure of one exterior angle of a regular polygon |
360/n |
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Parallelogram |
Definition: a quadrilateral with two sets of parallel sides Properties: opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, diagonals bisect eachother |
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Converses to prove a parallelogram |
if opposite sides are parallel (by definition), if opposite sides are congruent, if opposite angles are congruent, if diagonals bisect each other, if one pair of sides is congruent and parallel |
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Rectangle |
Definition: four right angles Properties: a parallelogram is congruent if and only if its diagonals are congruent and/or it has one right angle |
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Rhombus |
Definition: a quadrilateral with four congruent sides Properties: a parallelogram is a rhombus if and only if its diagonals are perpendicular and/or two consecutive sides are congruent |
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Square |
a quadrilateral with four right four congruent sides. a quadrilateral is a square if and only if it is a rectangle and a rhombus |
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Trapezoid |
Definition: a quadrilateral with one pair of parallel sides Properties: diagonals are congruent but don't bisect |
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Trapezoid Midsegment Theorem |
the midsegment of a trapezoid is parallel and half the sum of the bases |
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Kite |
Definition: Two pairs of consecutive sides are congruent Properties: a quadrilateral is a kite if and only if its diagonals are perpendicular and one pair of opposite angles are congruent |