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Angles and Lines, Euclidean Geometry 2020, Inductive Reasoning/Deductive Reasoning
Terms in this set (65)
Information provided in the problem
Congruent Supplements Theorem
If angles are supplementary to the same angle then those two angles are congruent
Congruent Complements Theorem
If angles are complementary to the same angle then those two angles are congruent
Two lines that intersect and form a right angle (90°)
A third line that intersects to others
Two lines on a plane that never meet. They are always the same distance apart.
Two nonparallel lines that not are not on same plane that do not intersect
Same side of transversal in similar positions. One point interior and one has to be exterior. They have equal measure.
Alternate Interior Angles
Interior angles on alternative sides of the transversal. All are equal.
Same-Side Interior Angles
Two points that are on the same side of the transversal and are inside of the parallel lines. They are Supplementary
Alternate Exterior Angles
parallel lines are cut by a transversal, then alternate exterior angles are congruent.
Alternate Exterior Angles Converse Theorem
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
alternate interior angles converse theorem
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
same side interior angles converse theorem
If two lines are cut by a transversal so the same side interior angles are supplementary, then the lines are parallel.
Same slope, different y-int
Perpendicular lines have slopes that are the opposite and the reciprocal of the original slope Normal: 1/2 Perpendicular: -2
Part of a line that consists of two endpoints
Two rays that have the same initial point
Extends forever in two directions
Two lines in the same plane that do not intersect
points on the same line
to divide into two equal parts
all angles are congruent
two angles whose measures have a sum of 90 degrees
two angles whose measures have a sum of 180 degrees
A point that divides a segment into two congruent segments
An exact location represented by a dot.
A part of a line, with one endpoint, that continues without end in one direction
A point where two or more straight lines meet.
Lines that intersect to form right angles
a flat surface that has no thickness and extends forever
arc of a circle
two points on the circle and the continuous part of the circle between the two points
The set of all points in a plane that are the same distance from a given point called the center
an opinion or conclusion formed on the basis of incomplete information
a specific case for which the conjecture is false
A style of proof in which the statements and reasons are presented in paragraph form.
Uses arrows to show the flow of the logical argument
a type of proof written as numbered statements and reasons that show the logical order of an argument
Addition, Subtraction, Multiplication, Division, Substitution, Reflexive, Symmetric, Transitive, Distributive
Addition and Subtraction Properties
For all numbers a, b, and c, if a=b, then a+c=b+c and a-c=b-c
Multiplication Property of Equality
If a=b, then ac=bc
Substitution Property of Equality
If a=b, then b can be substituted for a in any expression
Symmetric Property of Equality
if a=b, then b=a
If a=b and b=c, then a=c
Angle Addition Postulate
If P is in the interior of <RST, then m<RSP + m<PST = m<RST
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
reasoning based on observations and patterns
statement believed to be true based on inductive reasoning
evidence to proving a conjecture false
statement that can be written in form of 'if p then q'
the part of p of a conditional statement following the word if
the part of q of a conditional statement falling the word then
if p then q
if q then p
if not p then not q
if not q then not p
reasoning based on facts, logic, and definitions
A diagram that uses circles to display elements of different sets. Overlapping circles show common elements.
a convenient method for organizing the truth values of statements
a word that connects two or more words or sentences with the word and notated by p^q
a compound statement formed by joining two or more statements with the word or; notated by p v q
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Angles and Lines, Euclidean Geometry 202…
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Angles and Lines