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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

Midpoint Formula

((x#1+x#2)/2 , (y#1+y#2)/2)

Adjacent Angles

two angles that share a side and vertex but do not overlap

Linear Pair

two adjacent angles that form a straight line

Definition of Perpendicular

Lines intersect to form 90* angles

Regular Shape

Equilateral and Equiangular

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

Disjunction

an "or" statement

Logically Equivalent

two statements that have the same truth value

Disjunctive Syllogism (D.S.)

If one part of an "or" statement is false the other part must be true

Law of Syllogism (L.O.S.)

Given: If A then B, If B then C

Conclusion: If A then C


Conditional Statement

A statement in If-Then form

If part of a Conditional Statement

hypothesis

Then part of a Conditional Statement

conclusion

Converse

formed by switching the hypothesis and conclusion (can be true or false)

Inverse

formed by negating both the hypothesis and the conclusion (can be true or false)

Contrapositive

formed by combining the inverse and converse (same truth value as the original statement)

Bi-Conditional Statement

Contains the phrase "if and only if"


(only true if its true both ways)

An if-then statement is only false if...

the hypothesis is true and the conclusion is false (statements are true until proven false)

Law of Detachment

Given: If p then q, p


Conclusion: q

Postulate V. Theorem

Postulate - a statement that is accepted as true without proof


Theorem - a statement that can be proven true

Addition Property of Equality

If A=B, then A+C = B+C

Subtraction Property of Equality

If A=B, then A-C = B-C

Multiplication Property of Equality

If A=B, then AC = BC

Division Property of Equality

if A=B, then A/C = B/C

Symetric

The order of which things are equal/congruent is insignifigant

Definition of Congruent

used to switch things back and forth between congruent and equal

Transitive

If two things are congruent/equal to the same thing, then they are congruent/equal to each other

Substitution

If A=B, then B can be substituted for A in any equation (Cannot Be Used With Shapes)

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)

Angle Addition Postulate

m/_ABC+m/_CBD=m/_ABD

Linear Pair Postulate

if two angles form a linear pair, then they are supplementary

Congruent Supplements/Complements Theorem

Two angles that are complementary/supplementary to the same angle are congruent

Corresponding Angles Postulate

if two parallel lines are cut by a transversal, then the corresponding angles are congruent (the converse is also true)

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)

Consecutive Interior Angles Theorem

if two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary (converse is also true)

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

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

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

Triangle Sum Theorem

The sum of the interior measures of a triangle is 180*

Exterior Angle Theorem

the measure of one exterior angle of a triangle is equal to the sum of the opposing interior angles

Corollary

a statement that follows directly from a theorem

Third Angles Theorem

if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent

The Triangle Congruence Postulates that do not exist are

AAA, ASS, SSA

Perpendicular Bisector Theorem

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment (converse is also true)

Angle Bisector Theorem

any point on the angle bisector is equidistant from the sides of the angle


(converse is also true)

Circumcenter

formed by perpendicular bisectors, equidistant from the vertices

Incenter

formed by the angle bisectors, equidistant from the sides of the triangle

Centroid

formed by medians, center of mass. Distance from midpoint to side is 1/3 the entire median

Orthocenter

formed by altitudes, is useless

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"

Triangle Inequality Theorem

the sum of the lengths of any two side lengths is greater than that of the third side

Hinge Theorem

if two triangles have two pairs of congruent sides, then the triangle with the larger included angle has the longer third side

Sum of the Interior angles of a polygon with n sides

(n-2)180

the measure of one interior angle of a regular polygon

((n-2)180)/n

the sum of the exterior angles of a regular polygon is always...

360

the measure of one exterior angle of a regular polygon

360/n

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

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

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

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

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

Trapezoid

Definition: a quadrilateral with one pair of parallel sides


Properties: diagonals are congruent but don't bisect

Trapezoid Midsegment Theorem

the midsegment of a trapezoid is parallel and half the sum of the bases

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